Regional Controllability of Riemann–Liouville Time-Fractional Semilinear Evolution Equations

Abstract

In this paper, we discuss the exact regional controllability of fractional evolution equations involving Riemann–Liouville fractional derivative of order $q\in \left]\mathrm{0,1}\right[$ . The result is obtained with the help of the theory of fractional calculus, semigroup theory, and Banach fixed-point theorem under several assumptions on the corresponding linear system and the nonlinear term. Finally, some numerical simulations are given to illustrate the obtained result.