Adaptive Meir–Keeler Contractions in Double Controlled Metric Spaces: Theory and Applications to Caputo Fractional Equations

---

Aloqaily A., Mlaiki N., Abdeljawad T.

International Journal of Analysis and Applications, cilt.24, 2026 (ESCI, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 24
• Basım Tarihi: 2026
• Doi Numarası: 10.28924/2291-8639-24-2026-161
• Dergi Adı: International Journal of Analysis and Applications
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
• Anahtar Kelimeler: Caputo derivative, Double controlled metric type space, Fixed point theorem, Fractional differential equations, Meir–Keeler contraction
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

In this paper, we investigate fixed point results for a new class of Meir–Keeler type contractions in the setting of double controlled metric type spaces governed by two independent control functions. This framework strictly extends controlled metric type spaces and allows the treatment of nonlinear mappings that cannot be handled by a single control function. We establish existence and uniqueness fixed point theorems for generalized Meir–Keeler contractions in complete double controlled metric type spaces. As an application, we employ the obtained results to study the existence and uniqueness of solutions for nonlinear fractional differential equations involving the Caputo fractional derivative. Several illustrative examples, including non-Lipschitz nonlinearities, are provided to demonstrate the effectiveness of the proposed approach.