Work

Investigation of coupled system with double delay terms via an exponential kernel differential operator

Year: 2026

Type: article

Abstract: This work presents a detailed analysis of a coupled system of fractional delay differential equations involving an exponential kernel operator of Mittag-Leffler type. These models realistically capture complex epidemics and biological systems in which memory and time delays are essential. Our system in particular describes the simultaneous action of long-term memory and multiple distinct delays, as in incubation and immune-response lags in diseases. Using tools from functional analysis and contraction mapping theory, we prove the existence and uniqueness of solutions. We also study several Ulam-type stability notions, including Ulam-Hyers and Ulam-Hyers-Rassias stability, to evaluate the robustness of model predictions under small measurement errors or perturbations. Finally, a concrete numerical example confirms the theoretical framework and illustrates its practical applicability.

Source: Mathematical and Computer Modelling of Dynamical Systems

DOI: 10.1080/13873954.2025.2610964

Authors: Khaled Aldwoah, E. I. Hassan, Gulalai Bibi, Amjad Ali, Abdulghani Muhyi, W. E. Ahmed

Institutions: Islamic University of Madinah, Imam Mohammad ibn Saud Islamic University, University of Swat, Hajjah University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,533

Funders: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University, Al-Imam Muhammad Ibn Saud Islamic University