Abstract
In this work, we scrutinize the existence and uniqueness of the solution to the Integro differential equations for the Caputo fractional derivative on the time scale. We derive the solution of the neutral fractional differential equations along the finite delay conditions. The fixed point theory is demonstrated, and the solution depends upon the fixed point theorems: Banach contraction principle, nonlinear alternative for Leray-Schauder type, and Krasnoselskii fixed point theorem.