In this article, we consider the second‐order nonautonomous integro‐differential system with finite delay and noninstantaneous impulse. The aim of this paper is to establish the approximate controllability result for the proposed control problem. We use the evolution operator and Schauder's fixed‐point approach for proving our main result. Also, we provide an example to illustrate our main result.

In this manuscript, we have studied the coupled system of Hilfer fractional differential equations with non-local conditions. We have used the Leray-alternative Schauder’s and the Contraction principle to obtain the results on the existence and uniqueness of the solution of the proposed problem in the weighted space of continuous functions. For the defined problem, sufficient conditions have also been developed to determine the Ulam stability of the solution. The key conclusions are well-illustrated with examples.

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