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Research Article | Open Access

Ulam stability for nonlinear implicit differential equations with Hilfer-Katugampola fractional derivative and impulses

Soufyane Bouriah1, Mouffak Benchohra2, Juan J. Nieto3, Yong Zhou4,5( )
Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, P.O. Box 151 Chlef 02000, Algeria
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria
Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Abstract

In this paper, we investigate the existence, uniqueness and stability results for a class of nonlinear impulsive Hilfer-Katugampola problems. Our reasoning is founded on the Banach contraction principle and Krasnoselskii's fixed point theorem. In addition, an example is provided to demonstrate the effectiveness of the main results.

Keywords

Hilfer-Katugampola fractional derivativeinitial value problemexistenceuniquenessstabilityfixed pointimpulses
CLC number: 26A33

References

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12859-12884
DOI: 10.3934/math.2022712

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Cite this article:
Bouriah S, Benchohra M, Nieto JJ, et al. Ulam stability for nonlinear implicit differential equations with Hilfer-Katugampola fractional derivative and impulses. AIMS Mathematics, 2022, 7(7): 12859-12884. https://doi.org/10.3934/math.2022712

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Received: 26 November 2021
Revised: 04 April 2022
Accepted: 17 April 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)