An existence result involving both the generalized proportional Riemann-Liouville and Hadamard fractional integral equations through generalized Darbo's fixed point theorem

Abstract

<abstract><p>In this paper, we propose and prove an extension and generalization, which extends and generalizes the Darbo's fixed point theorem (DFPT) in the context of measure of noncompactness (MNC). Thereafter, we use DFPT to investigate the existence of solutions to mixed-type fractional integral equations (FIE), which include both the generalized proportional $ (\kappa, \tau) $-Riemann-Liouville and Hadamard fractional integral equations. We've included a suitable example to strengthen the article.</p></abstract>