Controllability of semilinear neutral fractional functional evolution equations with infinite delay

摘要

This paper is concerned with the semilinear differential system of fractional order with infinite delay: D~a x(t) = Ax(t) + Bu(t) + f (t,x_t), t ∈ [0, x(t) = (t), t ∈] — co, 0], with 1 < a < 2. We prove that the system is controllable when A generates an a-resolvent family (S_a(t))t>0 on a complex Banach space X and the control u ∈ L~2( [0, 7];X).