Existence and optimal control results for Caputo fractional delay Clark's subdifferential inclusions of order r∈(1,2) with sectorial operators

In this study, we investigate the effect of Clarke's subdifferential type on theoptimal control results for fractional differential systems of order 1<r<2withdelay. The main findings of this study are tested by using multivalued functions,sectorial operators, fractional derivatives, and the fixed point theorem. To begin,the existence of mild solutions is established and verified primarily by using avery well multivalued fixed point theorem and the characteristics of generalizedClarke subdifferential problems. Furthermore, we get a finding on the existenceof optimal control for the presented control system under particular reasonableconditions. After that, we will move on to the time optimal control results forthe given system. Finally, an example for drawing the theory behind the mainconclusions is shown.