Discontinuous solutions of delay fractional integral equation via measures of noncompactness

Abstract

This article considers the existence and the uniqueness of monotonic solutions of a delay functional integral equation of fractional order in the weighted Lebesgue space $ L_1^N({\mathbb{R}}^+) $. Our analysis uses a suitable measure of noncompactness, a modified version of Darbo's fixed point theorem, and fractional calculus in the mentioned space. An illustrated example to show the applicability and significance of our outcomes is included.

Keywords

• weighted lebesgue space
• delay fractional integral equations
• measure of noncompactness (m.n.c.)
• carathéodory conditions