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

<p>This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.</p>
</abstract>

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Laboratoire de Mathématique et Physique Appliquées

Laboratory of Pure and Applied Mathematics

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion...

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Published Online: Jan 21, 2022

Page range: 43 - 56

Received: Mar 05, 2021

Accepted: May 07, 2021

DOI: https://doi.org/10.2478/aupcsm-2021-0003

Keywords
fractional diffusion, generalized self-similar solution, blow-up, global existence, uniqueness

© 2021 Farid Nouioua et al., published by Sciendo

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

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Published Online: Jan 21, 2022

Page range: 43 - 56

Received: Mar 05, 2021

Accepted: May 07, 2021

DOI: https://doi.org/10.2478/aupcsm-2021-0003

Keywordsfractional diffusion, generalized self-similar solution, blow-up, global existence, uniqueness

© 2021 Farid Nouioua et al., published by Sciendo

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

Keywords
fractional diffusion, generalized self-similar solution, blow-up, global existence, uniqueness