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 $u\in L^{2}([0,T];\X)$.
Published
May 25, 2011
How to Cite
MOPHOU, Gisele M.; N'GUEREKATA, Gaston M.. Controllability of semilinear neutral fractional functional evolution equations with infinite delay. Nonlinear Studies, [S.l.], v. 18, n. 2, p. 195-209, may 2011. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/657>. Date accessed: 01 oct. 2016.
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Articles