Stability analysis for a class of implicit fractional differential equations with instantaneous impulses and Riemann-Liouville boundary conditions

Abstract

In this article some conditions are established for the existence and uniqueness regarding our proposed model, Implicit fractional differential equation with instantaneous impulses and Riemann-Liouville fractional integral boundary condition in view of Schafer's fixed point theorem.  The paper also discusses different types of Ulam's stability, i.e. Ulam-Hyers-stability, generalized Ulam-Hyers-stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the proposed model. An example is given to illustrate our main result.