Search results for: fractional edge domination number

Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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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: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Abdul Jamil Nazari, Shigeo Honma

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This paper evaluates and compares the effect of fractional flow curves on the heavy oil and light oil recoveries in a petroleum reservoir. Fingering of flowing water is one of the serious problems of the oil displacement by water and another problem is the estimation of the amount of recover oil from a petroleum reservoir. To address these problems, the fractional flow of heavy oil and light oil are investigated. The fractional flow approach treats the multi-phases flow rate as a total mixed fluid and then describes the individual phases as fractional of the total flow. Laboratory experiments are implemented for two different types of oils, heavy oil, and light oil, to experimentally obtain relative permeability and fractional flow curves. Application of the light oil fractional curve, which exhibits a regular S-shape, to the water flooding method showed that a large amount of mobile oil in the reservoir is displaced by water injection. In contrast, the fractional flow curve of heavy oil does not display an S-shape because of its high viscosity. Although the advance of the injected waterfront is faster than in light oil reservoirs, a significant amount of mobile oil remains behind the waterfront.

Keywords: fractional flow, relative permeability, oil recovery, water fingering

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: Muhammad Swilam

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Solutions for the wrong division problem of the Extended Multi-Modulus Divider (EMMD) that occurs during modulus extension (i.e. switching the modulus value between two different ranges of division ratios), in open loop fractional dividers and fractional multiplying delay locked loop, is proposed. A detailed study for the MMD with Sigma-Delta is also presented. Moreover, extensive simulations for the divider are presented to ensure and verify its functionality and compared with the conventional dividers.

Keywords: extended multi-modulus divider (EMMD), fractional multiplying delay locked loop, open loop fractional divider, sigma delta modulator

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Authors: Rana Gill, Chandandeep Kaur

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Segmentation of images can be implemented using different fundamental algorithms like edge detection (discontinuity based segmentation), region growing (similarity based segmentation), iterative thresholding method. A comprehensive literature review relevant to the study gives description of different techniques for vehicle number plate detection and edge detection techniques widely used on different types of images. This research work is based on edge detection techniques and calculating threshold on the basis of five edge operators. Five operators used are Prewitt, Roberts, Sobel, LoG and Canny. Segmentation of characters present in different type of images like vehicle number plate, name plate of house and characters on different sign boards are selected as a case study in this work. The proposed methodology has seven stages. The proposed system has been implemented using MATLAB R2010a. Comparison of all the five operators has been done on the basis of their performance. From the results it is found that Canny operators produce best results among the used operators and performance of different edge operators in decreasing order is: Canny>Log>Sobel>Prewitt>Roberts.

Keywords: segmentation, edge detection, text, extracting characters

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Authors: Kazim G. Atman, Hüseyin Sirin

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In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered.

Keywords: Einstein’s Coefficients, Fractional Calculus, Fractional Quantum Mechanics, Nonlocal Theories

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Authors: Yasser F. Hassan

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In this paper, a proposed model of cellular automata is studied by means of fractional integral function. A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. The paper discusses how using fractional integral function for representing cellular automata memory or state. The architecture of computing and learning model will be given and the results of calibrating of approach are also given.

Keywords: fractional integral, cellular automata, memory, learning

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Authors: Li Chen

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For an aerofoil or hydrofoil in high Reynolds number flows, broadband noise is generated efficiently as the result of the turbulence convecting over the trailing edge. This noise can be related to the surface pressure fluctuations, which can be predicted by either CFD or empirical models. However, in reality, the aerofoil or hydrofoil often operates at an angle of attack. Under this situation, the flow is subjected to an Adverse-Pressure-Gradient (APG), and as a result, a flow separation may occur. This study is to assess trailing-edge noise models for such flows. In the present work, the trailing-edge noise from a 2D airfoil at 6 degree of angle of attach is investigated. Under this condition, the flow is experiencing a strong APG, and the flow separation occurs. The flow over the airfoil with a chord of 300 mm, equivalent to a Reynold Number 4x10⁵, is simulated using RANS with the SST k-ɛ turbulent model. The predicted surface pressure fluctuations are compared with the published experimental data and empirical models, and show a good agreement with the experimental data. The effect of the APG on the trailing edge noise is discussed, and the associated trailing edge noise is calculated.

Keywords: aero-acoustics, adverse-pressure gradient, computational fluid dynamics, trailing-edge noise

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran

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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Ayub Khan, Net Ram Garg, Geeta Jain

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In this paper, backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.

Keywords: backstepping method, fractional order, synchronization, chaotic system

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

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The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Bode’s ideal transfer function, fractional calculus, fractional–order proportional integral (FOPI) controller, cascade control system

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Authors: Aquil Ahmed, Srikant Gupta, Irfan Ali

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In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Keywords: capacitated transportation problem, multi objective linear programming, multi-objective fractional programming, fuzzy goal programming, fuzzy sets, trapezoidal fuzzy number

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Authors: M. M. M. Jaradat

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For a given graph G, the set Ԑ of all subsets of E(G) forms an |E(G)| dimensional vector space over Z2 with vector addition X⊕Y = (X\Y ) [ (Y \X) and scalar multiplication 1.X = X and 0.X = Ø for all X, Yϵ Ԑ. The cycle space, C(G), of a graph G is the vector subspace of (E; ⊕; .) spanned by the cycles of G. Traditionally there have been two notions of minimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimum cycle basis (MCB) if its total length Σ BϵB |B| is minimum among all bases of C(G). The lexicographic product GρH has the vertex set V (GρH) = V (G) x V (H) and the edge set E(GρH) = {(u1, v1)(u2, v2)|u1 = u2 and v1 v2 ϵ E(H); or u1u2 ϵ E(G) and there is α ϵ Aut(H) such that α (v1) = v2}. In this work, a construction of a minimum cycle basis for the wreath product of wheels with paths is presented. Also, the length of the longest cycle of a minimum cycle basis is determined. Moreover, the basis number for the wreath product of the same is investigated.

Keywords: cycle space, minimum cycle basis, basis number, wreath product

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman

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This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which are unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples of the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.

Keywords: Sallen-Key, fractance, stability, low-pass filter, analog filter

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Authors: Bongsu Choi, Tae-Ho Song

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Vacuum insulation panel (VIP) is a promising thermal insulator for buildings, refrigerator, LNG carrier and so on. In general, it has the thermal conductivity of 2~4 mW/m•K. However, this thermal conductivity is that measured at the center of VIP. The total effective thermal conductivity of VIP is larger than this value due to the edge conduction through the envelope. In this paper, the edge conduction of VIP is examined theoretically, numerically and experimentally. To confirm the existence of the edge conduction, numerical analysis is performed for simple two-dimensional VIP model and a theoretical model is proposed to calculate the edge conductivity. Also, the edge conductivity is measured using the vacuum guarded hot plate and the experiment is validated against numerical analysis. The results show that the edge conductivity is dependent on the width of panel and thickness of Al-foil. To reduce the edge conduction, it is recommended that the VIP should be made as big as possible or made of thin Al film envelope.

Keywords: envelope, edge conduction, thermal conductivity, vacuum insulation panel

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Authors: A. Cherifi, B. S. Bouazza, A. O. Dahman, 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, fractional fourier transform, internet and information technology

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Authors: Dominic Roulx

Abstract:

Many scholars have in the past decade emphasized the relevance of Adorno’s criticism of the rationalized domination of nature (Naturbeherrschung) for thinking the environmental crisis. Beyond the intersubjective critical models of thinkers such as Habermas and Honneth, Adorno’s critical theory has the benefit, according to them, of disclosing the entwinement of social and natural domination in a critically productive way. The author will be arguing in this paper that Adorno’s model of critical theory displays a theoretical framework that is both original and relevant for thinking the ins and outs of the currentenvironmental crisis. To do so, he first construe Adorno’s understanding of the historical domination of nature and argue that Adorno’s method for its criticizing is immanent critique. He puts emphasis on how his understanding of the domination of nature implicitly implies an account of thedialectical relationship between reason and nature. In doing so, he presents a naturalistic understanding of his idea of the primacy of the object. Second, regarding Adorno’s concept of nature, he discusses what he sees as the shortcomings of many commentators’ understanding of the concept of nature in Adorno. He contends that they tend to fall short of Adorno’s concept of nature in failing to make sense of its thoroughly negative signification, thereby falling into an uncritical and fetichized comprehension of “nature. Third, he discusses the prospect for a possible “reconciliation” (Versöhnung) of nature with society. Highlighting how the domination of nature proves to produce the necessary conditions for its own overcoming, he contends that reconciliation with nature relies mainly on the subject’s capacity for critical self-reflection.

Keywords: german philosophy, adorno, nature, environmental crisis

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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

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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

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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

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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

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