Qualitative Analysis for a System of Generalized Caputo Proportional Fractional Integro-Differential Equations With Multiple Time Delays

Abstract

This study investigates a system of generalized Caputo proportional fractional delay integro-differential equations (CFDIDEs) involving multiple kernels and constant time delays. As key qualitative properties, the stability, asymptotic stability, exponential stability, and boundedness of solutions are analyzed through four newly established results. The results of the study are established using a suitable Lyapunov function, along with a modified Lyapunov–Razumikhin approach for the vector-valued case. The reliability and relevance of the proposed results are illustrated through two example implementations in particular cases of the system under consideration. The outcomes of this study makes new contributions to qualitative theory of CFDIDEs for vector-based cases. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.