Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions

Abstract

Abstract This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We establish some existence and uniqueness results for the given problem by applying the tools of fixed point theory. Furthermore, we investigate different kinds of stability such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. Finally, we give two examples to demonstrate the validity of main results.

Keywords

• Caputo derivative
• Riemann–Liouville integral
• Impulse
• Ulam–Hyers stability
• Fixed point theory