a study on analytic resolvent semilinear integro-differential equations with control functions

The goal of this research is to look at some of the sufficient conditions for approximate controllability in nonlinear resolvent integro-differential evolution control systems. we have considered that nonlinear term is satisfying lipschitz continuity. to show the key results, we employ gronwall’s inequality, semigroup theory, and the resolvent operators. the main results have been discussed under two sets of assumptions. application of common fixed point theorems such as banach, schauder, sadovskii, etc. is avoided as discussed earlier by several researchers in the available literature. finally, one case study based on the proposed problem is discussed in order to verify the theoretical findings.