Approximate boundary controllability for some stochastic partial functional integrodifferential equations with finite delay and Rosenblatt process

Abstract This study explores the approximate boundary controllability of certain nonlinear stochastic partial functional integrodifferential equations with finite delay and Rosenblatt process. By assuming that the linear undelayed component is approximately controllable and possesses a resolvent operator as defined by Grimmer, the research utilizes the Banach fixed-point theorem and the uniform norm-topology continuity of the resolvent operator to establish sufficient conditions for the system’s approximate controllability. This approach generalizes several significant results existing in the literature without necessitating the compactness of the resolvent operator or the uniform boundedness of the nonlinear term. An illustrative example is provided to demonstrate the applicability of the findings.