Measure of Noncompactness for Nonlinear Hilfer Fractional Differential Equation in Banach Spaces

Abstract

This paper deals with nonlinear fractional differential equation with boundary value problem conditions. We investigate the existence of solutions in Banach spaces with Hilfer derivative. To obtain such result we apply Monch's fixed point theorem and the technique of measures of noncompactness. An example illustrating the theory is given.