Mild solutions of Riemann–Liouville fractional differential equations with fractional impulses

Abstract

We consider Riemann–Liouville fractional differential equations with fractional-order derivative in the impulsive conditions. We study the existence of the mild solution by applying the Laplace transform method and (a,k)-regularized resolvent operator. We use the contraction mapping principle and fixed point theorem for condensing map to prove our existence results.