Existence of Mild Solutions for Fractional Integrodifferential Equations with Hilfer Derivatives

In this paper, we study the existence of solutions for fractional integrodifferential equations with Hilfer derivatives. We establish some new existence theorems for mild solutions by using Schaefer’s fixed-point theorem, a measure of noncompactness, and the resolvent operators associated with almost sectorial operators. Our results improve and extend many known results in the relevant references by removing some strong assumptions. Furthermore, we propose new nonlocal initial conditions for Hilfer evolution equations and study the existence of mild solutions to nonlocal problems.