Existence of solution for Hilfer fractional differential equations with boundary value conditions

Abstract

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of continuous functions. Then we obtain the existence results for a given problem under a new approach and minimal assumptions on nonlinear function f. The technique used in the analysis relies on a variety of tools including Schauder, Schaefer and Krasnoselski fixed point theorems. We demonstrate our results through illustrative examples.