Results on existence of solutions in nonlocal partial functional integrodifferential equations with finite delay in nondense domain

In this work, to show the existence and uniqueness solution of functional integrodifferential equation with nonlocal condition and finite delay function. This article contains continuously dependence of integral solution and existence of strict solution established by using integrated resolvent operator theory with support of Lipschitz continuous. In this article the operator (T(t))t⩾0 is assumed the locally Lipschitz continuous integrated resolvent operator and proved the existence of strict solution on reflexive and general Banach spaces. Finally an example is given related to this work.