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

Soufyane Bouriah; Mouffak Benchohra; Juan J. Nieto; Yong Zhou; Soufyane Bouriah; Mouffak Benchohra; Juan J. Nieto; Yong Zhou

doi:10.3934/math.2022712

AIMS Mathematics

2022, Volume 7, Issue 7: 12859-12884. doi: 10.3934/math.2022712

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

1.
Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, P.O. Box 151 Chlef 02000, Algeria
2.
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria
3.
Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
4.
Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
5.
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received: 26 November 2021 Revised: 04 April 2022 Accepted: 17 April 2022 Published: 05 May 2022
MSC : 26A33

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.
- Hilfer-Katugampola fractional derivative,
- initial value problem,
- existence,
- uniqueness,
- stability,
- fixed point,
- impulses
Citation: Soufyane Bouriah, Mouffak Benchohra, Juan J. Nieto, Yong Zhou. Ulam stability for nonlinear implicit differential equations with Hilfer-Katugampola fractional derivative and impulses[J]. AIMS Mathematics, 2022, 7(7): 12859-12884. doi: 10.3934/math.2022712

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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.

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