Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

Approximate controllability of impulsive system involving state-dependent delay and variable delay in control via fundamental solution

This article is concerned with the approximate controllability for a new class of impulsive semilinear control systems involving state-dependent delay and variable delay in control in Hilbert spaces. We formulate new sufficient conditions which guarantee the existence of solution to the considered system. We use the theory of fundamental solution, Krasnoselskii?s and Schauder?s fixed point theorems to establish our major results. Finally, two examples are constructed which demonstrate the effectiveness of obtained results.