Spectral method for solution of the fractional transport equation

Kadem, Abdelouahab; Luchko, Yury; Băleanu, Dumitru

doi:10.1016/s0034-4877(10)80026-6

Cited by 26 publications

(14 citation statements)

References 18 publications

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“…Povstenko suggested the fractional heat conduction equation [4], and Vázquez gave the second law of thermodynamics with fractional derivative [5]. Lutz considered the fractional transport equation for Levy stable processes [6], and Kadem et al discussed its solution using the spectral method [7]. Laskin presented the fractional Schrodinger equation [8], and Muslih et al suggested its solution [9].…”

Section: Introductionmentioning

confidence: 99%

Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow

Li¹,

Wang²,

Zeng³

et al. 2014

Advances in Mathematical Physics

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We discuss the line partial differential equations arising in fractal vehicular traffic flow. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. The obtained results show the efficiency and accuracy of implements of the present method.

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Section: Introductionmentioning

confidence: 99%

Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow

Li¹,

Wang²,

Zeng³

et al. 2014

Advances in Mathematical Physics

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“…Therefore, numerical and approximation techniques have been used for solving these equations. Some of the most common methods are homotopy perturbation method [39], Haar wavelet method [40], Spline collocation method [41], fractional difference method (FDM) [42], power series method [43], Adomian decomposition method (ADM) [44], Kronecker convolution product [45], spectral methods [46], He's variational iteration method [47], and homotopy analysis method [48].…”

Section: Fractional Kinetic Equation Model and Numerical Methodsmentioning

confidence: 99%

Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction

Ghaemi

Yunus

Ahmadian

et al. 2013

Abstract and Applied Analysis

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In view of the usefulness and a great importance of the kinetic equation in specific chemical engineering problems, we discuss the numerical solution of a simple fuzzy fractional kinetic equation applied for the hemicelluloses hydrolysis reaction. The fuzzy approximate solution is derived based on the Legendre polynomials to the fuzzy fractional equation calculus. Moreover, the complete error analysis is explained based on the application of fuzzy Caputo fractional derivative. The main advantage of the present method is its superior accuracy which is obtained by using a limited number of Legendre polynomials. The method is computationally interesting, and the numerical results demonstrate the effectiveness and validity of the method for solving fuzzy fractional differential equations.

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“…In the time-independent case, an analytical solution of the space-fractional radiative transport equation was found 15 . In this section we solve (1).…”

Section: Legendre-polynomial Expansionmentioning

confidence: 99%

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

Machida

2017

Journal of Mathematical Physics

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We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

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Spectral method for solution of the fractional transport equation

Cited by 26 publications

References 18 publications

Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow

Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow

Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

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