Affiliation:
1. Department of Mathematics, Université de M’sila , M’sila , Algeria
Abstract
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).
Subject
Psychiatry and Mental health
Reference35 articles.
1. Aleem, Maryam, et al. “On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz-Caputo operator.” Adv. Difference Equ. (2021): Paper No. 303. Cited on 50, 52, 53 and 54.
2. Almeida Ricardo. “A Gronwall inequality for a general Caputo fractional operator.” Arxiv (2017): arxiv.org/pdf/1705.10079.pdf. Cited on 51 and 52.
3. Almeida, Ricardo, Agnieszka B. Malinowska, and Tatiana Odzijewicz. “Fractional differential equations with dependence on the Caputo–Katugampola derivative.” J. Comput. Nonlinear Dynam. 11, no. 6 (2016): Paper No. 061017. Cited on 50.
4. Arioua, Yacine, Bilal Basti, and Nouredine Benhamidouche. “Initial value problem for nonlinear implicit fractional differential equations with Katugampola derivative.” Appl. Math. E-Notes 19 (2019): 397-412. Cited on 50.
5. Arioua, Yacine, and Maria Titraoui. “Boundary value problem for a coupled system of nonlinear fractional differential equations involving Erdélyi-Kober derivative.” Appl. Math. E-Notes 21 (2021): 291-306. Cited on 50.