On abstract Hilfer fractional integrodifferential equations with boundary conditions

Abstract

In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵ-approximate solutions.

Keywords

• Hilfer fractional integrodifferential equations
• Boundary conditions
• Mönch fixed point theorem
• Measure of noncompactness
• Existence
• Continuous dependence