ON LOCALLY ATTRACTIVE SOLUTIONS FOR QUADRATIC FRACTIONAL INTEGRAL EQUATIONS
Gulf Journal of Mathematics, cilt.24, sa.1, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.56947/22esbb56
- Dergi Adı: Gulf Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Anahtar Kelimeler: Banach algebra. 2020 Mathematics Subject Classification. Primary 26A33, 34A12, existence result, fixed point theorem, locally attractive solution, Quadratic functional fractional integral equation, Secondary 45G15
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
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.