Abstract
We study the asymptotic behavior of solutions of nonlinear fractional evolution equations in Banach spaces. Asymptotically almost periodic solutions on half line are obtained by establishing a sharp estimate on the resolvent operator family of evolution equations. In particular, when the semigroup generated by A is exponentially stable then the conditions of the existence asymptotically almost periodic solutions is satisfied. An application to a fractional partial differential equation with initial boundary condition is also considered.
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