Existence Results of Global Solutions for a Coupled Implicit Riemann-Liouville Fractional Integral Equation via the Vector Kuratowski Measure of Noncompactness

Abstract

The main goal of this study is to demonstrate an existence result of a coupled implicit Riemann-Liouville fractional integral equation. First, we prove a new fixed point theorem in spaces with an extended norm structure. That theorem generalized Darbo’s theorem associated with the vector Kuratowski measure of noncompactness. Second, we employ our obtained fixed point theorem to investigate the existence of solutions to the coupled implicit fractional integral equation on the generalized Banach space C([0,1],R)×C([0,1],R).

Keywords

• coupled implicit Riemann-Liouville fractional integral equation
• generalized Banach space
• fixed point theorems
• <i>M</i>-set contractive
• generalized measure of noncompactness