Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation

Povstenko, Yuriy; Kyrylych, Tamara

doi:10.3390/e19070297

Cited by 22 publications

(15 citation statements)

References 79 publications

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“…Finite element multigrid method for multi-term time fractional advection diffusion equations was given in [17]. Two approximate results in two different generalizations of the space-time-fractional advection diffusion equation were discussed in [18]. The fundamental solutions were obtained by the Laplace transform and Fourier transform, and the numerical results were also obtained.…”

Section: Introductionmentioning

confidence: 99%

Difference numerical solutions for time-space fractional advection diffusion equation

2019

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In this paper, a time-space fractional advection diffusion equation is considered for the natural extension of the convection diffusion equation. An explicit difference scheme and an implicit difference scheme are presented. The stability and convergence of the two difference schemes are discussed. It is shown that the explicit difference scheme is conditionally stable and convergent, and the implicit difference scheme is unconditionally stable and convergent. The convergence order of the two methods is O(τ + h).

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Section: Introductionmentioning

confidence: 99%

Difference numerical solutions for time-space fractional advection diffusion equation

2019

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“…A significant portion of fractional calculus theory is the two-dimensional fractional differential equations and integral equations which have further been studied in the articles [43,[45][46][47][48]. In [12], the authors have solved the two-dimensional fractional percolation equation in a non-homogeneous porous med-ium.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

et al. 2020

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In the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

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“…In [15], the Laplace and Fourier transforms were utilized to determine the analytical solutions of fractional advection-diffusion equation with time fractional Caputo-Fabrizio derivative. Povstenko and Kyrylych [16] discussed two approaches to obtaining the space-time fractional advection-diffusion equations. In this paper, Caputo time fractional derivative and Riesz fractional Laplacian were used.…”

Section: Introductionmentioning

confidence: 99%

A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection–diffusion equation

et al. 2018

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In this paper, we investigate a fully implicit finite difference scheme for solving the time fractional advection-diffusion equation. The time fractional derivative is estimated using Caputo's formulation, and the spatial derivatives are discretized using extended cubic B-spline functions. The convergence and stability of the fully implicit scheme are analyzed. Numerical experiments conducted indicate that the scheme is feasible and accurate.

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Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation

Cited by 22 publications

References 79 publications

Difference numerical solutions for time-space fractional advection diffusion equation

Difference numerical solutions for time-space fractional advection diffusion equation

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection–diffusion equation

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