This paper presents both a periodic and an asymptotic periodic solution for coupled Sylvester matrix Volterra integro-dynamic systems on time scales. The vectorization operator first changes the Sylvester matrix into the Kronecker product of the system. We then used Schauder’s fixed point theorem to determine a periodic existence solution for the system. Finally, we got solutions that were periodic and asymptotically periodic. Our system’s analysis brings together discrete and continuous dynamic systems.
Harisha et al. (Thu,) studied this question.