Approximate controllability of second-order nonlocal impulsive partial functional integro-differential evolution systems in Banach spaces

Abstract

This manuscript is involved with a class of second-order impulsive partial functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome.

Approximate controllability of time‐varying measure differential problem of second order with state‐dependent delay and noninstantaneous impulses

“…The results on approximate controllability for time-varying dynamical systems are limited. Nagaraj et al [13] developed approximate controllability for a time-varying differential system governed by second order via the Leray-Schauder nonlinear alternative. In earlier studies [14,15], the authors utilized Schauder's FPT to establish approximate controllability of a second-order nonautonomous systems having finite delay and NIIs.…”

Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse

“…The resluts on approximate controllability for time varying dynamical systems is limited. Nagaraj et al 13 developed approximate controllability for a time-varying differential system governed by second order via the Leray-Schauder nonlinear alternative. In 14,15 the authors utilized Schauder's FPT to establish approximate controllability of a second order non-autonomous systems having finite delay and NII.…”