Existence of solutions for semilinear fractional integro-differential equations with nonlocal conditions

Abstract

In this work, we consider the existence of solutions for semilinear fractional integrodifferential equations with nonlocal conditions. A new set of sufficient conditions proving existence of solutions are derived by using the fractional calculus, α-resolvent operators theory, measure of noncompactness and some fixed point theorems. In the end, an example is provided to illustrate the applicability of our results.