Ulam-Hyers stability for conformable fractional integro-differential impulsive equations with the antiperiodic boundary conditions

Fan Wan; Xiping Liu; Mei Jia; Fan Wan; Xiping Liu; Mei Jia

doi:10.3934/math.2022338

AIMS Mathematics

2022, Volume 7, Issue 4: 6066-6083. doi: 10.3934/math.2022338

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Research article

Ulam-Hyers stability for conformable fractional integro-differential impulsive equations with the antiperiodic boundary conditions

College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

Received: 26 October 2021 Revised: 21 December 2021 Accepted: 30 December 2021 Published: 17 January 2022
MSC : 34A08, 34B37, 34D20

This paper focuses on the stability for a class of conformable fractional impulsive integro-differential equations with the antiperiodic boundary conditions. Firstly, the existence and uniqueness of solutions of the integro-differential equations are studied by using the fixed point theorem under the condition of nonlinear term increasing at most linearly. And then, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for the boundary value problems are discussed by using the nonlinear functional analysis method and constraining related parameters. Finally, an example is given out to illustrate the applicability and feasibility of our main conclusions. It is worth mentioning that the stability studied in this paper highlights the role of boundary conditions. This method of studying stability is effective and can be applied to the study of stability for many types of differential equations.
Citation: Fan Wan, Xiping Liu, Mei Jia. Ulam-Hyers stability for conformable fractional integro-differential impulsive equations with the antiperiodic boundary conditions[J]. AIMS Mathematics, 2022, 7(4): 6066-6083. doi: 10.3934/math.2022338

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Abstract

This paper focuses on the stability for a class of conformable fractional impulsive integro-differential equations with the antiperiodic boundary conditions. Firstly, the existence and uniqueness of solutions of the integro-differential equations are studied by using the fixed point theorem under the condition of nonlinear term increasing at most linearly. And then, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for the boundary value problems are discussed by using the nonlinear functional analysis method and constraining related parameters. Finally, an example is given out to illustrate the applicability and feasibility of our main conclusions. It is worth mentioning that the stability studied in this paper highlights the role of boundary conditions. This method of studying stability is effective and can be applied to the study of stability for many types of differential equations.

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