ON LOCALLY ATTRACTIVE SOLUTIONS FOR QUADRATIC FRACTIONAL INTEGRAL EQUATIONS
Gulf Journal of Mathematics, vol.24, no.1, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 24 Issue: 1
- Publication Date: 2026
- Doi Number: 10.56947/22esbb56
- Journal Name: Gulf Journal of Mathematics
- Journal Indexes: Scopus
- Keywords: Banach algebra. 2020 Mathematics Subject Classification. Primary 26A33, 34A12, existence result, fixed point theorem, locally attractive solution, Quadratic functional fractional integral equation, Secondary 45G15
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Gelisim University Affiliated: Yes
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.