Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative-Reference-Cited by-同舟云学术

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Published:2019-01-01 Issue:1 Volume:52 Page:437-450
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Benchohra Mouffak¹,Bouriah Soufyane²,Nieto Juan J.³

Affiliation:

1. Laboratory of Mathematics , Djillali Liabes University of Sidi Bel-Abbes , P.O. Box 89 Sidi Bel Abbes 22000 , Algeria ; Department of Mathematics, College of Science , King Saud University , P.O. Box 2455, Riyadh 11451 , Saudi Arabia

2. Department of Mathematics Faculty of Exact Sciences and Informatics Hassiba Benbouali University , P.O. Box 151 Chlef 02000 , Algeria ; E-mail: s.bouriah@univ-chlef.dz

3. Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matemáticas , Universidade de Santiago de Compostela , Santiago de Compostela , Spain

Abstract

Abstract In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2019-0032/pdf

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