Fractional-Order Delayed Epidemic Models in Memory-Based Probabilistic Controlled Metric Spaces via Fixed Point Theory
International Journal of Analysis and Applications, vol.24, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 24
- Publication Date: 2026
- Doi Number: 10.28924/2291-8639-24-2026-195
- Journal Name: International Journal of Analysis and Applications
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Keywords: delay dynamics, epidemic modeling, fixed point, fractional-order systems, memory-based metric space, probabilistic contraction
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Gelisim University Affiliated: Yes
Abstract
We introduce memory-based probabilistic controlled metric spaces and establish a non-Markovian contraction principle that extends the Banach fixed point theorem by depending on a finite number of previous iterates. This framework is suited for systems with delay, hereditary effects, and fractional dynamics. We prove unique existence and convergence of Picard iterations under memory-based probabilistic contractions. As an application, we analyze a fractional-order delayed epidemic model with memory and incubation effects, showing convergence to a unique equilibrium. These results provide a unified tool for fractional epidemic dynamics with delay and memory.