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

Abstract

Abstract 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.

Keywords

• Approximate controllability
• Hemivariational inequalities
• Fractional evolution inclusions
• Mainardi’s Wright-type function
• Generalized Clarke’s subdifferential