An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators

Abstract

In this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed point theorem. Initially, we introduce the idea of mild solution for fractional hemivariational inequalities. Next, the approximate controllability results of semilinear control problems were then established. Moreover, we will move on to the system involving nonlocal conditions. Finally, an example is provided in support of the main results we acquired.

Keywords

• hemivariational inequalities
• fractional derivative
• approximate controllability
• sectorial operators
• mild solution
• generalized Clarke’s subdifferential