Ulam-Hyers-Rassias stability for a class of nonlinear implicit Hadamard fractional integral boundary value problem with impulses

Kaihong Zhao; Shuang Ma; Kaihong Zhao; Shuang Ma

doi:10.3934/math.2022175

AIMS Mathematics

2022, Volume 7, Issue 2: 3169-3185. doi: 10.3934/math.2022175

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Research article

Ulam-Hyers-Rassias stability for a class of nonlinear implicit Hadamard fractional integral boundary value problem with impulses

Kaihong Zhao ^,,
Shuang Ma

Department of Mathematics, Kunming University of Science and Technology, Yunnan, Kunming 650500, China

Received: 12 October 2021 Accepted: 22 November 2021 Published: 25 November 2021
MSC : 34A08, 34B10, 34B37, 34D20

This paper considers a class of nonlinear implicit Hadamard fractional differential equations with impulses. By using Banach's contraction mapping principle, we establish some sufficient criteria to ensure the existence and uniqueness of solution. Furthermore, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of this system are obtained by applying nonlinear functional analysis technique. As applications, an interesting example is provided to illustrate the effectiveness of main results.
- Hadamard fractional integral BVP,
- existence and uniqueness,
- stability,
- contraction mapping principle
Citation: Kaihong Zhao, Shuang Ma. Ulam-Hyers-Rassias stability for a class of nonlinear implicit Hadamard fractional integral boundary value problem with impulses[J]. AIMS Mathematics, 2022, 7(2): 3169-3185. doi: 10.3934/math.2022175

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Abstract

This paper considers a class of nonlinear implicit Hadamard fractional differential equations with impulses. By using Banach's contraction mapping principle, we establish some sufficient criteria to ensure the existence and uniqueness of solution. Furthermore, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of this system are obtained by applying nonlinear functional analysis technique. As applications, an interesting example is provided to illustrate the effectiveness of main results.

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