Unique mild solution for caputo's fractional perturbed evolution equations with state-dependent delay

. This study examines if there are any mild solutions for the perturbed partial functional and neutral functional evolution equations with statedependent delay when the derivative utilizes Caputo's fractional derivative, as well as whether any such solutions are unique. The solution itself determines how long the equations take to solve. The work proves the existence and uniqueness of these solutions using semigroup theory and the Banach contraction theorem in Banach spaces.