Inverse Problem for Abstract Differential Equation With Noninstantaneous Impulses

We consider an inverse problem for first order abstract noninstantaneous impulsive differential equation in a Banach space and identifies the parameter using an overdetermined condition on a mild solution. A direct approach using Volterra integral equations for sufficiently regular data and an optimal control approach for less regular data are the main techniques to find the result. Under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original inverse problem. At last, an example is provided in the support of our results.