Optimal Controls for a Class of Conformable Fractional Evolution Systems

Abstract

In the scale of abstract Banach spaces, the existence as well as the controllability are considered for a class of evolution systems involving conformable fractional derivatives. Under essential conditions on nonlinearity, among other conditions, existence theorems are obtained by employing the operator semigroup theory. The existence problem of optimal state-control pairs is further studied by establishing a minimize sequence twice. Two examples are given as applications of the abstract results.

Keywords

• conformable fractional derivatives
• evolution systems
• mild solutions
• optimal controls
• the operator semigroup theory