<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve fractional mathematical problem of diffusion by Chebyshev collocation method which turns the original problems into the system of fractional ordinary differential and algebraic equations by imposing orthogonality property. This system is solved by implementing Finite difference method. The numerical illustrations confirm that the combination of these two methods allow us to establish one of the best truncated solution in the series form.</p>
</abstract>

Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve fractional mathematical problem of diffusion by Chebyshev collocation method which turns the original problems into the system of fractional ordinary differential and algebraic equations by imposing orthogonality property. This system is solved by implementing Finite difference method. The numerical illustrations confirm that the combination of these two methods allow us to establish one of the best truncated solution in the series form.

On new aspects of Chebyshev polynomials for space-time fractional diffusion process

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this...

On new aspects of Chebyshev polynomials for space-time fractional diffusion process

Publié en ligne: 31 mars 2023

Pages: 1051 - 1062

Reçu: 18 sept. 2022

Accepté: 19 déc. 2022

DOI: https://doi.org/10.2478/amns.2021.2.00327

Mots clés
Chebyshev collocation method, space-time fractional diffusion equation, Finite differences, Caputo derivatives

© 2023 Ali Demir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On new aspects of Chebyshev polynomials for space-time fractional diffusion process

Publié en ligne: 31 mars 2023

Pages: 1051 - 1062

Reçu: 18 sept. 2022

Accepté: 19 déc. 2022

DOI: https://doi.org/10.2478/amns.2021.2.00327

Mots clésChebyshev collocation method, space-time fractional diffusion equation, Finite differences, Caputo derivatives

© 2023 Ali Demir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Chebyshev collocation method, space-time fractional diffusion equation, Finite differences, Caputo derivatives