Nonlinear impulsive fractional differential equation with Atangana-Baleanu-Caputo derivative: Nonlinear impulsive fractional equations with ABC derivative

Abstract

In this work, we study the existence and uniqueness of solutions to a class of fractional differential equations of ABC type with impulse conditions. Sufficient conditions are established to prove the existence results by using fixed point theorems such as the Banach contraction principle and the Schauder fixed point theorem. In addition, the Ulam stability of the solution is considered. Finally, an example is provided to illustrate the main results.