On Locally Attractive Solutions for Quadratic Fractional Integral Equations

Abstract

In this paper, we investigate the existence and attractivity of solutions for ψ-fractional-order quadratic functional integral equations in a Banach algebra over ℝ₊=[0,∞). Using Dhage's hybrid fixed point theorem and appropriate analytical techniques, we establish existence results ensuring the well-posedness of the considered equations under suitable assumptions. The main novelty lies in deriving existence and local attractivity results for a coupled quadratic functional integral structure governed by ψ-fractional operators within a Banach algebra framework, extending beyond classical fractional and non-quadratic models. Two illustrative examples validate the applicability and effectiveness of the proposed approach, providing further insight into the qualitative analysis of fractional integral equations.