Controllability of semilinear neutral fractional functional evolution equations with infinite delay
Gisele M. Mophou
Gaston M. N'Guerekata
Abstract
This paper is concerned with the semilinear differential system of fractional order with infinite delay: $D^\alpha\,x(t)=Ax(t)+Bu(t)+f(t,x_t),~~t\in [0,T],$ $x(t)=\phi(t)$, $t\in ]-\infty,0]$, with $1\alpha2$. We prove that the system is controllable when $A$ generates an $\alpha$-resolvent family $(S_\alpha(t))_{t\geq 0}$ on a complex Banach space $\X$ and the control $u\in L^{2}([0,T];\X)$.