An extension of the singular boundary method for solving two dimensional time fractional diffusion equations

Rivaz, Azim; Yousefi, Farzane

doi:10.1016/j.enganabound.2017.07.009

Cited by 4 publications

(2 citation statements)

References 36 publications

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“…Over the past few decades, fractional differential equation (FDM) models have become an increasingly important tool for physics, finance, materials, control, viscoelasticity, chaos, bioengineering and engineering to understand and make predictions about how phenomena functions evolve through time and space [1][2][3][4]. In [5] Baleanu and et.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

Ramezani

2021

Int. J. Appl. Comput. Math

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The main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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Section: Introductionmentioning

confidence: 99%

Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

Ramezani

2021

Int. J. Appl. Comput. Math

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“…Over the past few decades, fractional differential equation models have become an increasingly important tool for science and engineering to understand and make predictions about how phenomena function and evolve through time and space. [1][2][3][4] Baleanu et al 5 studied an iteration scheme based on the local fractional Laplace variation iteration method (LFLVIM) and developed an iterative scheme for the exact solutions of local fractional wave equations (LFWEs). Khan et al 6 presented numerical solutions of fractional differential equations the fractional-order Brusselator and used Bernstein polynomials.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis nonlinear multi‐term time fractional differential equation with collocation method via fractional B‐spline

Ramezani

2019

Math Methods in App Sciences

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In this work, we present numerical analysis for nonlinear multi‐term time fractional differential equation which involve Caputo‐type fractional derivatives for 0<αi<1,i=1,2,⋯, double-struckN. The proposed method is based on utilization of fractional B‐spline basics in collocation method. The scheme can be readily obtained efficient and quite accurate with less computational work numerical result. The proposal approach transform nonlinear multi‐term time fractional differential equation into a suitable linear system of algebraic equations which can be solved by a suitable numerical method. The numerical experiments will be verify to demonstrate the effectiveness of our method for solving one‐ and two‐dimensional multi‐term time fractional differential equation.

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Coupling of the improved singular boundary method and dual reciprocity method for multi-term time-fractional mixed diffusion-wave equations

Safari

Chen

2019

Computers & Mathematics with Applications

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An extension of the singular boundary method for solving two dimensional time fractional diffusion equations

Cited by 4 publications

References 36 publications

Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

Numerical analysis nonlinear multi‐term time fractional differential equation with collocation method via fractional B‐spline

Coupling of the improved singular boundary method and dual reciprocity method for multi-term time-fractional mixed diffusion-wave equations

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