Measure of noncompactness and fractional integro-differential equations with state-dependent nonlocal conditions in Fréchet spaces

Abstract

This paper deals with the existence of mild solutions for non-linear fractional integrodifferential equations with state-dependent nonlocal conditions. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application of the main result has been included.

Keywords

• fractional integro-differential equations
• solution operator
• mild solution
• fixed point
• state-dependent nonlocal condition
• measure of noncompactness
• fréchet space