Dynamics and stability for Katugampola random fractional differential equations

Fouzia Bekada; Saïd Abbas; Mouffak Benchohra; Juan J. Nieto; Fouzia Bekada; Saïd Abbas; Mouffak Benchohra; Juan J. Nieto

doi:10.3934/math.2021503

AIMS Mathematics

2021, Volume 6, Issue 8: 8654-8666. doi: 10.3934/math.2021503

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Research article

Dynamics and stability for Katugampola random fractional differential equations

1.
Laboratory of Mathematics, University of Saïda-Dr. Moulay Tahar, P. O. Box 138, EN-Nasr, 20000 Saïda, Algeria
2.
Department of Mathematics, University of Saïda-Dr. Moulay Tahar, P. O. Box 138, EN-Nasr, 20000 Saïda, Algeria
3.
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P. O. Box 89, Sidi Bel-Abbès 22000, Algeria
4.
Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

Received: 15 January 2021 Accepted: 27 May 2021 Published: 07 June 2021
MSC : 26A33, 34A37, 34G20

This paper deals with some existence of random solutions and the Ulam stability for a class of Katugampola random fractional differential equations in Banach spaces. A random fixed point theorem is used for the existence of random solutions, and we prove that our problem is generalized Ulam-Hyers-Rassias stable. An illustrative example is presented in the last section.
- differential equation,
- Katugampola fractional integral,
- Katugampola fractional derivative,
- random solution,
- Banach space,
- Ulam stability,
- fixed point
Citation: Fouzia Bekada, Saïd Abbas, Mouffak Benchohra, Juan J. Nieto. Dynamics and stability for Katugampola random fractional differential equations[J]. AIMS Mathematics, 2021, 6(8): 8654-8666. doi: 10.3934/math.2021503

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Abstract

This paper deals with some existence of random solutions and the Ulam stability for a class of Katugampola random fractional differential equations in Banach spaces. A random fixed point theorem is used for the existence of random solutions, and we prove that our problem is generalized Ulam-Hyers-Rassias stable. An illustrative example is presented in the last section.

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