Asymptotic periodicity in nonlinear coupled matrix Sylvester Volterra systems integro-dynamic system on arbitrary time domains

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.