Fractional-Order Delayed Epidemic Models in Memory-Based Probabilistic Controlled Metric Spaces via Fixed Point Theory
International Journal of Analysis and Applications, cilt.24, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24
- Basım Tarihi: 2026
- Doi Numarası: 10.28924/2291-8639-24-2026-195
- Dergi Adı: International Journal of Analysis and Applications
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Anahtar Kelimeler: delay dynamics, epidemic modeling, fixed point, fractional-order systems, memory-based metric space, probabilistic contraction
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
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.