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

<p>In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity variable <italic>η</italic>, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).</p>
</abstract>

In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity variable η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).

Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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

In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation....

Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative

Pubblicato online: 03 lug 2023

Pagine: 49 - 74

Ricevuto: 27 dic 2022

Accettato: 03 apr 2023

DOI: https://doi.org/10.2478/aupcsm-2023-0005

© 2023 Nora Ouagueni et al., published by Sciendo

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