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

<p>This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.</p>
</abstract>

This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.

Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the...

Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation

Published Online: Sep 21, 2023

Page range: 349 - 359

Received: Oct 12, 2022

Accepted: Apr 12, 2023

DOI: https://doi.org/10.34768/amcs-2023-0025

Keywords
anomalous diffusion, fractional diffusion equations, fractional calculus, difference equations

© 2023 Agnieszka B. Malinowska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation

Published Online: Sep 21, 2023

Page range: 349 - 359

Received: Oct 12, 2022

Accepted: Apr 12, 2023

DOI: https://doi.org/10.34768/amcs-2023-0025

Keywordsanomalous diffusion, fractional diffusion equations, fractional calculus, difference equations

© 2023 Agnieszka B. Malinowska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
anomalous diffusion, fractional diffusion equations, fractional calculus, difference equations