Ulam-type stability for a class of implicit fractional differential equations with non-instantaneous integral impulses and boundary condition

Abstract

Abstract In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions for the existence and uniqueness of solutions for such a class of fractional differential equations using Caputo fractional derivative. The arguments are based on generalized Diaz-Margolis’s fixed point theorem. We provide two examples, which shows the validity of our main results.

Keywords

• Caputo fractional derivative
• implicit fractional differential equations
• fractional integral
• non-instantaneous impulses
• Ulam-type stability
• Diaz-Margolis’s fixed point theorem