Search results for: tempered fractional

Authors: Fouzi Aboura

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The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s.

Keywords: FOPID controller, fractional order, AVR system, objective function, optimization, GA, PSO, HGAPSO

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Authors: Swati Tyagi, Syed Abbas

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Fractional-order Hopfield neural networks are generally used to model the information processing among the interacting neurons. To show the constancy of the processed information, it is required to analyze the stability of these systems. In this work, we perform Mittag-Leffler stability for the corresponding Caputo fractional-order bidirectional associative memory (BAM) neural networks with various time-delays. We derive sufficient conditions to ensure the existence and uniqueness of the equilibrium point by using the theory of topological degree theory. By applying the fractional Lyapunov method and Mittag-Leffler functions, we derive sufficient conditions for the global Mittag-Leffler stability, which further imply the global asymptotic stability of the network equilibrium. Finally, we present two suitable examples to show the effectiveness of the obtained results.

Keywords: bidirectional associative memory neural network, existence and uniqueness, fractional-order, Lyapunov function, Mittag-Leffler stability

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: S. Ghoudelbourk, A. Omeiri, D. Dib, H. Cheghib

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This paper shows that we can improve the performance of the auto-adjustable electric machines if a fractional dynamic is considered in the algorithm of the controlling order. This structure is particularly interested in the separate control of active and reactive power of the double-fed induction generator (DFIG) of wind power conversion chain. Fractional regulators are used in the regulation of chain of powers. Knowing that, usually, the source of DFIG is provided by converters through controlled rectifiers, all this system makes the currents of lines strongly polluted that can have a harmful effect for the connected loads and sensitive equipment nearby. The solution to overcome these problems is to replace the power of the rotor DFIG by multilevel inverters supplied by PV which improve the THD. The structure of the adopted adjustment is tested using Matlab/Simulink and the results are presented and analyzed for a variable wind.

Keywords: DFIG, fractional regulator, multilevel inverters, PV

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

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The FOPI controller is proposed based on the main properties of the decoupling control scheme, as well as the fractional calculus. By using the simplified decoupling technique, the transfer function of decoupled apparent process is firstly separated into a set of n equivalent independent processes in terms of a ratio of the diagonal elements of original open-loop transfer function to those of dynamic relative gain array and the fraction – order PI controller is then developed for each control loops due to the Bode’s ideal transfer function that gives the desired fractional closed-loop response in the frequency domain. The simulation studies were carried out to evaluate the proposed design approach in a fair compared with the other existing methods in accordance with the structured singular value (SSV) theory that used to measure the robust stability of control systems under multiplicative output uncertainty. The simulation results indicate that the proposed method consistently performs well with fast and well-balanced closed-loop time responses.

Keywords: ideal transfer function of bode, fractional calculus, fractional order proportional integral (FOPI) controller, decoupling control system

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Authors: F. Hamidi, N. Amiri, H. Mishmast Nehi

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The Bilevel Programming (BP) model has been presented for a decision making process that consists of two decision makers in a hierarchical structure. In fact, BP is a model for a static two person game (the leader player in the upper level and the follower player in the lower level) wherein each player tries to optimize his/her personal objective function under dependent constraints; this game is sequential and non-cooperative. The decision making variables are divided between the two players and one’s choice affects the other’s benefit and choices. In other words, BP consists of two nested optimization problems with two objective functions (upper and lower) where the constraint region of the upper level problem is implicitly determined by the lower level problem. In real cases, the coefficients of an optimization problem may not be precise, i.e. they may be interval. In this paper we develop an algorithm for solving interval bilevel linear fractional programming problems. That is to say, bilevel problems in which both objective functions are linear fractional, the coefficients are interval and the common constraint region is a polyhedron. From the original problem, the best and the worst bilevel linear fractional problems have been derived and then, using the extended Charnes and Cooper transformation, each fractional problem can be reduced to a linear problem. Then we can find the best and the worst optimal values of the leader objective function by two algorithms.

Keywords: best and worst optimal solutions, bilevel programming, fractional, interval coefficients

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Authors: Samaneh Rahimirshnani, Hossein Jafari

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In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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Authors: Muhammad Abdullah, Asma Rashid Butt, Nauman Raza

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Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs.

Keywords: viscous fluid, magnetic particles, fractional calculus, laplace transformation

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Authors: Keltoum Chahour, Mickael Binois

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Due to a lack of standardization during the invasive fractional flow reserve (FFR) procedure, the index is subject to many sources of uncertainties. In this paper, we investigate -through simulation- the effect of the (FFR) device position and configuration on the obtained value of the (FFR) fraction. For this purpose, we use computational fluid dynamics (CFD) in a 3D domain corresponding to a diseased arterial portion. The (FFR) pressure captor is introduced inside it with a given length and coefficient of bending to capture the (FFR) value. To get over the computational limitations, basically, the time of the simulation is about 2h 15min for one (FFR) value; we generate a Gaussian Process (GP) model for (FFR) prediction. The (GP) model indicates good accuracy and demonstrates the effective error in the measurement created by the random configuration of the pressure captor.

Keywords: fractional flow reserve, Gaussian processes, computational fluid dynamics, drift

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Authors: Kizito Ugochukwu Nwajeri

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This paper presents a distinct approach to solving fractional dynamical systems using hybrid block methods (HBMs). Fractional calculus extends the concept of derivatives and integrals to non-integer orders and finds increasing application in fields such as physics, engineering, and finance. However, traditional numerical techniques often struggle to accurately capture the complex behaviors exhibited by these systems. To address this challenge, we develop HBMs that integrate single-step and multi-step methods, enabling the simultaneous computation of multiple solution points while maintaining high accuracy. Our approach employs polynomial interpolation and collocation techniques to derive a system of equations that effectively models the dynamics of fractional systems. We also directly incorporate boundary and initial conditions into the formulation, enhancing the stability and convergence properties of the numerical solution. An adaptive step-size mechanism is introduced to optimize performance based on the local behavior of the solution. Extensive numerical simulations are conducted to evaluate the proposed methods, demonstrating significant improvements in accuracy and efficiency compared to traditional numerical approaches. The results indicate that our hybrid block methods are robust and versatile, making them suitable for a wide range of applications involving fractional dynamical systems. This work contributes to the existing literature by providing an effective numerical framework for analyzing complex behaviors in fractional systems, thereby opening new avenues for research and practical implementation across various disciplines.

Keywords: fractional calculus, numerical simulation, stability and convergence, Adaptive step-size mechanism, collocation methods

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Authors: Birs Isabela, Muresan Cristina, Folea Silviu, Prodan Ovidiu

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The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.

Keywords: fractional order control, piezoelectric actuators, smart beam, vibration suppression

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Baghdad Said

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Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces.

Keywords: SFDE, SD, UHRS, MNCs, FPT

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Authors: Muhammad Fiaz

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The article in hand is the study of complex features like Zero Hopf Bifurcation, Chaos and Synchronization of integer and fractional order version of a new 3D finance system. Trusted tools of averaging theory and active control method are utilized for investigation of Zero Hopf bifurcation and synchronization for both versions respectively. Inventiveness of the paper is to find the answer of a question that is it possible to find a chaotic system which can be synchronized with any other of the same dimension? Based on different examples we categorically develop a theory that if a couple of master and slave chaotic dynamical system is synchronized by selecting a suitable gain matrix with special conditions then the master system is synchronized with any chaotic dynamical system of the same dimension. With the help of this study we developed generalized theorems for synchronization of n-dimension dynamical systems for integer as well as fractional versions. it proposed that this investigation will contribute a lot to control dynamical systems and only a suitable gain matrix with special conditions is enough to synchronize the system under consideration with any other chaotic system of the same dimension. Chaotic properties of fractional version of the new finance system are also analyzed at fractional order q=0.87. Simulations results, where required, also provided for authenticity of analytical study.

Keywords: complex analysis, chaos, generalized synchronization, control dynamics, fractional order analysis

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Authors: Dávid Kovács, Bálint Csanády, Dániel Boros, Iván Ivkovic, Lóránt Nagy, Dalma Tóth-Lakits, László Márkus, András Lukács

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The modeling practice of financial instruments has seen significant change over the last decade due to the recognition of time-dependent and stochastically changing correlations among the market prices or the prices and market characteristics. To represent this phenomenon, the Stochastic Correlation Process (SCP) has come to the fore in the joint modeling of prices, offering a more nuanced description of their interdependence. This approach has allowed for the attainment of realistic tail dependencies, highlighting that prices tend to synchronize more during intense or volatile trading periods, resulting in stronger correlations. Evidence in statistical literature suggests that, similarly to the volatility, the SCP of certain stock prices follows rough paths, which can be described using fractional differential equations. However, estimating parameters for these equations often involves complex and computation-intensive algorithms, creating a necessity for alternative solutions. In this regard, the Fractional Ornstein-Uhlenbeck (fOU) process from the family of fractional processes offers a promising path. We can effectively describe the rough SCP by utilizing certain transformations of the fOU. We employed neural networks to understand the behavior of these processes. We had to develop a fast algorithm to generate a valid and suitably large sample from the appropriate process to train the network. With an extensive training set, the neural network can estimate the process parameters accurately and efficiently. Although the initial focus was the fOU, the resulting model displayed broader applicability, thus paving the way for further investigation of other processes in the realm of financial mathematics. The utility of SCP extends beyond its immediate application. It also serves as a springboard for a deeper exploration of fractional processes and for extending existing models that use ordinary Wiener processes to fractional scenarios. In essence, deploying both SCP and fractional processes in financial models provides new, more accurate ways to depict market dynamics.

Keywords: fractional Ornstein-Uhlenbeck process, fractional stochastic processes, Heston model, neural networks, stochastic correlation, stochastic differential equations, stochastic volatility

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Authors: U. Sabura Banu, S. K. Lakshmanaprabu

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The improvement of meta-heuristic algorithm encourages control engineer to design an optimal controller for industrial process. Most real-world industrial processes are non-linear multivariable process with high interaction. Even in sub-process unit, thousands of loops are available mostly interacting in nature. Optimal controller design for such process are still challenging task. Closed loop controller design by multiloop PID involves a tedious procedure by performing interaction study and then PID auto-tuning the loop with higher interaction. Finally, detuning the controller to accommodate the effects of the other process variables. Fractional order PID controllers are replacing integer order PID controllers recently. Design of Multiloop Fractional Order (MFO) PID controller is still more complicated. Cuckoo algorithm, a swarm intelligence technique is used to optimally tune the MFO PID controller with easiness minimizing Integral Time Absolute Error. The closed loop performance is tested under servo, regulatory and servo-regulatory conditions.

Keywords: Cuckoo algorithm, mutliloop fractional order PID controller, two Interacting conical tank process

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

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Authors: S. Gupta, R. Sarkar, S. Pathak, D. H. Kela, A. Pramanick, P. Talukdar

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Low alloy quenched and tempered steels are typically used in cast railway components such as knuckles, yokes, and couplers. Since these components experience extensive impact loading during their service life, adequate impact toughness of these grades need to be ensured to avoid catastrophic failure of parts in service. Because of the general availability of Charpy V Test equipment, Charpy test is the most common and economical means to evaluate the impact toughness of materials and is generally used in quality control applications. With this backdrop, an experiment was designed to evaluate the effect of austenitizing temperature, soaking time and resultant grain size on the Charpy impact toughness and the related fracture mechanisms in a quenched and tempered low alloy steel, with the aim of optimizing the heat treatment parameters (i.e. austenitizing temperature and soaking time) with respect to impact toughness. In the first phase, samples were austenitized at different temperatures viz. 760, 800, 840, 880, 920 and 960°C, followed by quenching and tempering at 600°C for 4 hours. In the next phase, samples were subjected to different soaking times (0, 2, 4 and 6 hours) at a fixed austenitizing temperature (980°C), followed by quenching and tempering at 600°C for 4 hours. The samples corresponding to different test conditions were then subjected to instrumented Charpy tests at -40°C and energy absorbed were recorded. Subsequently, microstructure and fracture surface of samples corresponding to different test conditions were observed under scanning electron microscope, and the corresponding grain sizes were measured. In the final stage, austenitizing temperature, soaking time and measured grain sizes were correlated with impact toughness and the fracture morphology and mechanism.

Keywords: heat treatment, grain size, microstructure, retained austenite and impact toughness

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Authors: Mario Robinson, Moe Rabea

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This research examines the effects of heat treatment processes on the mechanical properties and corrosion resistanceof1045 and 4140 Steel Alloysfor industrial applications. Heat treatment processes of full annealing, normalizing, quenching, and tempering are carried out on the alloy samples. The mechanical and corrosion resistance tests of the heat treated samples are carried out, and the results obtained are related to their SEMmorphologies analysis. The results show that the heat treatment processes have an effect on the tensile strength, impact, and a significant effect on the corrosion resistance of the alloy samples. With respect to the strain characteristics, significant improvement in the ductility of the samples is recorded in the full annealing and alloy tempered samples. Thus, for application requiring strength and ductility, such as in aerospace industries, this tempered heat treated alloy could be used. In addition, the quenched sample shows a significant improvement in hardness.

Keywords: heat treatment, corrosion resistance, steel, industrial appilcations

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Authors: Asma Hanif, A. I. K. Butt, Shabir Ahmad, Rahim Ud Din, Mustafa Inc

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This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.

Keywords: Caputo fractional derivative, existence and uniqueness, gronwall inequality, Lyapunov theory

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu

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A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: cancer model, fractional calculus, numerical simulations, stability analysis

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Ali Motalebi Saraji, Reza Zarei Lamuki

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Speed control and behavior improvement of permanent magnet synchronous motors (PMSM) that have reliable performance, low loss, and high power density, especially in industrial drives, are of great importance for researchers. Because of its importance in this paper, coefficients optimization of proportional-integrator-derivative fractional order controller is presented using Particle Swarm Optimization (PSO) algorithm in order to improve the behavior of PMSM in its speed control loop. This improvement is simulated in MATLAB software for the proposed optimized proportional-integrator-derivative fractional order controller with a Genetic algorithm and compared with a full order controller with a classic optimization method. Simulation results show the performance improvement of the proposed controller with respect to two other controllers in terms of rising time, overshoot, and settling time.

Keywords: speed control loop of permanent magnet synchronous motor, fractional and full order proportional-integrator-derivative controller, coefficients optimization, particle swarm optimization, improvement of behavior

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Authors: Mohamed Habireche, Nacer E. Bacha, Mohamed Djeghdjough

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In the brick industry, smooth double roll crusher is used for medium and fine crushing of soft to medium hard material. Due to opposite inward rotation of the rolls, the feed material is nipped between the rolls and crushed by compression. They are subject to intense wear, known as three-body abrasion, due to the action of abrasive products. The production downtime affecting productivity stems from two sources: the bi-monthly rectification of the roll crushers and their replacement when they are completely worn out. Choosing the right material for the roll crushers should result in longer machine cycles, and reduced repair and maintenance costs. All roll crushers are imported from outside Algeria. This results in sometimes very long delivery times which handicap the brickyards, in particular in respecting delivery times and honored the orders made by customers. The aim of this work is to investigate the effect of alloying additions on microstructure and wear behavior of grey lamellar cast iron for smooth roll crushers in brick industry. The base gray iron was melted in an induction furnace with low frequency at a temperature of 1500 °C, in which return cast iron scrap, new cast iron ingot, and steel scrap were added to the melt to generate the desired composition. The chemical analysis of the bar samples was carried out using Emission Spectrometer Systems PV 8050 Series (Philips) except for the carbon, for which a carbon/sulphur analyser Elementrac CS-i was used. Unetched microstructure was used to evaluate the graphite flake morphology using the image comparison measurement method. At least five different fields were selected for quantitative estimation of phase constituents. The samples were observed under X100 magnification with a Zeiss Axiover T40 MAT optical microscope equipped with a digital camera. SEM microscope equipped with EDS was used to characterize the phases present in the microstructure. The hardness (750 kg load, 5mm diameter ball) was measured with a Brinell testing machine for both treated and as-solidified condition test pieces. The test bars were used for tensile strength and metallographic evaluations. Mechanical properties were evaluated using tensile specimens made as per ASTM E8 standards. Two specimens were tested for each alloy. From each rod, a test piece was made for the tensile test. The results showed that the quenched and tempered alloys had best wear resistance at 400 °C for alloyed grey cast iron (containing 0.62%Mn, 0.68%Cr, and 1.09% Cu) due to fine carbides in the tempered matrix. In quenched and tempered condition, increasing Cu content in cast irons improved its wear resistance moderately. Combined addition of Cu and Cr increases hardness and wear resistance for a quenched and tempered hypoeutectic grey cast iron.

Keywords: casting, cast iron, microstructure, heat treating

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Hector Carcel Luis Alberiko Gil-Alana

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This paper examines the time series behavior of three variables (GDP, Price level of Consumption and Population) in the eight countries that belong to the West African Economic and Monetary Union (WAEMU), which are Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Senegal and Togo. The reason for carrying out this study lies in the considerable heterogeneity that can be perceived in the data from these countries. We conduct a long memory and fractional integration modeling framework and we also identify potential breaks in the data. The aim of the study is to perceive up to which degree the eight West African countries that belong to the same monetary union follow the same economic patterns of stability. Testing for mean reversion, we only found strong evidence of it in the case of Senegal for the Price level of Consumption, and in the cases of Benin, Burkina Faso and Senegal for GDP.

Keywords: West Africa, Monetary Union, fractional integration, economic patterns

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Authors: Bello Yusuf Idi

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The Gongola arm of the Upper Banue Trough, Northeastern Nigeria is predominantly covered by the outcrops of Limestone-bearing rocks in form of Sandstone with intercalation of carbonate clay, shale, basaltic, felsphatic and migmatide rocks at subpixel dimension. In this work, subpixel classification algorithm was used to classify the data acquired from landsat 7 Enhance Thematic Mapper (ETM+) satellite system with the aim of producing fractional distribution image for three most economically important solid minerals of the area: Limestone, Basalt and Migmatide. Linear Spectral Unmixing (LSU) algorithm was used to produce fractional distribution image of abundance of the three mineral resources within a 100Km2 portion of the area. The results show that the minerals occur at different proportion all over the area. The fractional map could therefore serve as a guide to the ongoing reconnaissance for the economic potentiality of the formation.

Keywords: linear spectral un-mixing, upper benue trough, gongola arm, geological engineering

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Authors: Victor Manuel Alcántara Alza

Abstract:

The way in which the application of the deep cryogenic treatment DCT(-196°C) affects, applied with subsequent aging, was investigated, regarding the mechanical properties of hardness, toughness and microstructure, applied to martensitic stainless steels, with the aim of establishing a different methodology compared to the traditional DCT cryogenic treatment with subsequent tempering. For this experimental study, a muffle furnace was used, first subjecting the specimens to deep cryogenization in a liquid Nitrogen bath/4h, after being previously austenitized at the following temperatures: 1020-1030-1040-1050 (°C) / 1 hour; and then tempered in oil. A first group of cryogenic samples were subjected to subsequent aging at 150°C, with immersion times: 2.5 -5- 10 - 20 - 50 – 100 (h). The next group was subjected to subsequent tempering at temperatures: 480-500-510-520-530-540 (°C)/ 2h. The hardness tests were carried out under standards, using a Universal Durometer, and the readings were made on the HRC scale. The Impact Resistance tests were carried out in a Charpy machine following the ASTM E 23 – 93ª standard. Measurements were taken in joules. Microscopy was performed at the optical level using a 1000X microscope. It was found: For the entire aging interval, the samples austenitized at 1050°C present greater hardness than austenitized at 1040°C, with the maximum peak aged being at 30h. In all cases, the aged samples exceed the hardness of the tempered samples, even in their minimum values. In post-tempered samples, the tempering temperature hardly have effect on the impact strength of material. In the Cryogenic Treatment: DCT + subsequent aging, the maximum hardness value (58.7 HRC) is linked to an impact toughness value (54J) obtained with aging time of 39h, which is considered an optimal condition. The higher hardness of steel after the DCT treatment is attributed to the transformation of retained austenite into martensite. The microstructure is composed mainly of lath martensite; and the original grain size of the austenite can be appreciated. The choice of the combination: Hardness-toughness, is subject to the required service conditions of steel.

Keywords: deep cryogenic treatment; aged precipitation; martensitic steels;, mechanical properties; martensitic steels, hardness, carbides precipitaion

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