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

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.

Keywords

• conformable fractional derivative
• integro-differential impulsive equations
• antiperiodic boundary conditions
• existence and uniqueness
• ulam-hyers stability
• ulam-hyers-rassias stability