Search results for: fractional caputo derivative
529 Certain Results of a New Class of Meromorphic Multivalent Functions Involving Ruscheweyh Derivative
Authors: Kassim A. Jassim
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In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product
Procedia PDF Downloads 336528 A New Approach for Generalized First Derivative of Nonsmooth Functions Using Optimization
Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor
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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions
Procedia PDF Downloads 557527 Melnikov Analysis for the Chaos of the Nonlocal Nanobeam Resting on Fractional-Order Softening Nonlinear Viscoelastic Foundations
Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane
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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.Keywords: chaos, fractional-order, Melnikov method, nanobeam
Procedia PDF Downloads 159526 Hermite–Hadamard Type Integral Inequalities Involving k–Riemann–Liouville Fractional Integrals and Their Applications
Authors: Artion Kashuri, Rozana Liko
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In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.Keywords: Hermite-Hadamard's inequalities, Hölder's inequality, k-Riemann-Liouville fractional integral, special means
Procedia PDF Downloads 127525 Numerical Solution of Space Fractional Order Solute Transport System
Authors: Shubham Jaiswal
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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system
Procedia PDF Downloads 261524 Solution of Nonlinear Fractional Programming Problem with Bounded Parameters
Authors: Mrinal Jana, Geetanjali Panda
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In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.Keywords: fractional programming, interval valued function, interval inequalities, partial order relation
Procedia PDF Downloads 519523 B Spline Finite Element Method for Drifted Space Fractional Tempered Diffusion Equation
Authors: Ayan Chakraborty, BV. Rathish Kumar
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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional
Procedia PDF Downloads 192522 Equalization Algorithm for the Optical OFDM System Based on the Fractional Fourier Transform
Authors: A. Cherifi, B. Bouazza, A. O. Dahmane, B. Yagoubi
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Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.Keywords: OFDM, (FrFT) fractional fourier transform, optical OFDM, equalization algorithm
Procedia PDF Downloads 430521 Dynamical Analysis of the Fractional-Order Mathematical Model of Hashimoto’s Thyroiditis
Authors: Neelam Singha
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The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots.Keywords: adomian decomposition method, fractional derivatives, Hashimoto's thyroiditis, mathematical modeling
Procedia PDF Downloads 211520 Approximations of Fractional Derivatives and Its Applications in Solving Non-Linear Fractional Variational Problems
Authors: Harendra Singh, Rajesh Pandey
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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis
Procedia PDF Downloads 298519 Observer-Based Leader-Following Consensus of Nonlinear Fractional-Order Multi-Agent Systems
Authors: Ali Afaghi, Sehraneh Ghaemi
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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs
Procedia PDF Downloads 398518 Lie Symmetry Treatment for Pricing Options with Transactions Costs under the Fractional Black-Scholes Model
Authors: B. F. Nteumagne, E. Pindza, E. Mare
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We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.Keywords: fractional brownian model, symmetry, transaction cost, option pricing
Procedia PDF Downloads 399517 Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising
Authors: Jianwei Ma, Diriba Gemechu
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In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.Keywords: anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, split Bregman algorithm
Procedia PDF Downloads 207516 Design of Wide-Range Variable Fractional-Delay FIR Digital Filters
Authors: Jong-Jy Shyu, Soo-Chang Pei, Yun-Da Huang
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In this paper, design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters is proposed. With respect to the conventional VFD filter which is designed such that its delay is adjustable within one unit, the proposed VFD FIR filter is designed such that its delay can be tunable within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this paper, least-squares method is adopted to design WR-VFD FIR filter. Throughout this paper, several examples will be proposed to demonstrate the effectiveness of the presented methods.Keywords: digital filter, FIR filter, variable fractional-delay (VFD) filter, least-squares approximation
Procedia PDF Downloads 491515 Using Derivative Free Method to Improve the Error Estimation of Numerical Quadrature
Authors: Chin-Yun Chen
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Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.Keywords: numerical quadrature, error estimation, derivative free method, interval computation
Procedia PDF Downloads 463514 Separate Powers Control Structure of DFIG Based on Fractional Regulator Fed by Multilevel Inverters DC Bus Voltages of a photovoltaic System
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
Procedia PDF Downloads 401513 Analytical Design of Fractional-Order PI Controller for Decoupling Control System
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
Procedia PDF Downloads 331512 Derivative Usage, Ownership Structure, and Bank Value in European Countries
Authors: Chuang-Chang Chang, Keng-Yu Ho, Yu-Jen Hsiao, Hsin-Ni Yang
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Using a sample of detailed ownership data of 1,032 listed commercial bank observations in 30 European countries from 2004 to 2010, we explore what categories of shareholder are more likely to use derivatives and how different types of owners affect the bank value. We find that a shift in equity from bank investors to either non-financial companies or institutional investors have increase incentives to use derivatives. Moreover, we have significant evidence that a shift in equity from bank investors to either family or manager shareholders who attend derivative activities will decrease bank value. However, a shift in equity from bank investors to non-financial companies who use derivative instrument will increase the bank value. Our results are also robustness to address for the potential endogeneity problems.Keywords: derivative usage, ownership structure, bank value
Procedia PDF Downloads 348511 Interval Bilevel Linear Fractional Programming
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
Procedia PDF Downloads 446510 Covariance of the Queue Process Fed by Isonormal Gaussian Input Process
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
Procedia PDF Downloads 62509 Numerical Solution of Magneto-Hydrodynamic Flow of a Viscous Fluid in the Presence of Nanoparticles with Fractional Derivatives through a Cylindrical Tube
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
Procedia PDF Downloads 206508 Virtual Assessment of Measurement Error in the Fractional Flow Reserve
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
Procedia PDF Downloads 134507 On the Solution of Fractional-Order Dynamical Systems Endowed with Block Hybrid Methods
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
Procedia PDF Downloads 43506 Fractional Order Controller Design for Vibration Attenuation in an Airplane Wing
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
Procedia PDF Downloads 314505 Chaos Analysis of a 3D Finance System and Generalized Synchronization for N-Dimension
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
Procedia PDF Downloads 68504 Fast Estimation of Fractional Process Parameters in Rough Financial Models Using Artificial Intelligence
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
Procedia PDF Downloads 118503 An Antibacterial Dental Restorative Containing 3,4-Dichlorocrotonolactone: Synthesis, Formulation and Evaluation
Authors: Dong Xie, Leah Howard, Yiming Weng
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The objective of this study was to synthesize and characterize 5-acryloyloxy-3,4-dichlorocrotonolactone (a furanone derivative), use this derivative to modify a dental restorative, and study the effect of the derivative on the antibacterial activity and compressive strength of the formed restorative. In this study, a furanone derivative was synthesized, characterized, and used to formulate a dental restorative. Compressive strength (CS) and S. mutans viability were used to evaluate the mechanical strength and antibacterial activity of the formed restorative. The fabricated restorative specimens were photocured and conditioned in distilled water at 37oC for 24 h, followed by direct testing for CS or/and incubating with S. mutans for 48 h for antibacterial testing. The results show that the modified dental restorative showed a significant antibacterial activity without substantially decreasing the mechanical strengths. With addition of the antibacterial derivative up to 30%, the restorative kept its original CS nearly unchanged but showed a significant antibacterial activity with 68% reduction in the S. mutans viability. Furthermore, the antibacterial function of the modified restorative was not affected by human saliva. The aging study also indicates that the modified restorative may have a long-lasting antibacterial function. It is concluded that this experimental antibacterial restorative may potentially be developed into a clinically attractive dental filling restorative due to its high mechanical strength and antibacterial function.Keywords: antibacterial, dental restorative, compressive strength, S. mutans viability
Procedia PDF Downloads 326502 Multiloop Fractional Order PID Controller Tuned Using Cuckoo Algorithm for Two Interacting Conical Tank Process
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
Procedia PDF Downloads 498501 Online Robust Model Predictive Control for Linear Fractional Transformation Systems Using Linear Matrix Inequalities
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
Procedia PDF Downloads 395500 Assessment of Pre-Processing Influence on Near-Infrared Spectra for Predicting the Mechanical Properties of Wood
Authors: Aasheesh Raturi, Vimal Kothiyal, P. D. Semalty
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We studied mechanical properties of Eucalyptus tereticornis using FT-NIR spectroscopy. Firstly, spectra were pre-processed to eliminate useless information. Then, prediction model was constructed by partial least squares regression. To study the influence of pre-processing on prediction of mechanical properties for NIR analysis of wood samples, we applied various pretreatment methods like straight line subtraction, constant offset elimination, vector-normalization, min-max normalization, multiple scattering. Correction, first derivative, second derivatives and their combination with other treatment such as First derivative + straight line subtraction, First derivative+ vector normalization and First derivative+ multiplicative scattering correction. The data processing methods in combination of preprocessing with different NIR regions, RMSECV, RMSEP and optimum factors/rank were obtained by optimization process of model development. More than 350 combinations were obtained during optimization process. More than one pre-processing method gave good calibration/cross-validation and prediction/test models, but only the best calibration/cross-validation and prediction/test models are reported here. The results show that one can safely use NIR region between 4000 to 7500 cm-1 with straight line subtraction, constant offset elimination, first derivative and second derivative preprocessing method which were found to be most appropriate for models development.Keywords: FT-NIR, mechanical properties, pre-processing, PLS
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