Controllability of semilinear neutral fractional functional evolution equations with infinite delay

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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 $u\in L^{2}([0,T];\X)$.

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2011-05-25

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How to Cite

Controllability of semilinear neutral fractional functional evolution equations with infinite delay. (2011). Nonlinear Studies, 18(2). https://nonlinearstudies.com/index.php/nonlinear/article/view/657