Adaptive Meir–Keeler Contractions in Double Controlled Metric Spaces: Theory and Applications to Caputo Fractional Equations
International Journal of Analysis and Applications, vol.24, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 24
- Publication Date: 2026
- Doi Number: 10.28924/2291-8639-24-2026-161
- Journal Name: International Journal of Analysis and Applications
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Keywords: Caputo derivative, Double controlled metric type space, Fixed point theorem, Fractional differential equations, Meir–Keeler contraction
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Gelisim University Affiliated: Yes
Abstract
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.