Total Controllability of Non-Autonomous Measure Evolution Systems with Non-Instantaneous Impulses and State-Dependent Delay

Abstract

This paper is concerned with the existence of mild solutions and total controllability for a class of non-autonomous measure evolution systems with non-instantaneous impulses and state-dependent delay. By using the theory of evolution family and Krasnoselskii’s fixed point theorem, the existence of mild solutions and total controllability for the considered systems is obtained. Finally, we give two applications to support the validity of the study.

Controllability of fractional measure evolution systems with state-dependent delay and nonlocal condition

“…Moreover, the physical meaning of fractional order models is clearer and simpler than that of integer order differential models when simulating complex mechanical problems. For detailed results on fractional calculus, see [19,22,20,21,24,26,27,31,32,40,41,43,39,45,48] and references therein. However, most of the existing controllability works on MDEs are devoted to integer order measure evolution systems.…”