Periodic Boundary Value problem for the Dynamical system with neutral integro-differential equation on time scales

Examining the results of existence and Ulam stability in a fractional dynamic system, including a neutral integro-differential equation that incorporates periodic boundary conditions on time scales and the Caputo fractional nabla derivative, is the main objective of the study. Standard fixed-point techniques are applied to obtain the results. Additionally, controllability and Ulam stability results are included. The application of the theoretical results is illustrated with a suitable example.