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On almost automorphic mild solutions for fractional semilinear initial value problems. (English) Zbl 1189.34079
Summary: This paper investigates almost automorphic mild solutions of the fractional semilinear equation $D\alpha x(t)=Ax(t)+f(t,x(t))$, $0<\alpha <1$, considered in a Banach space $X$, where $A$ is a linear operator of sectorial type $\omega <0$. Some sufficient conditions are given for the existence, uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation.

##### MSC:
 34C27 Almost and pseudo-almost periodic solutions of ODE 26A33 Fractional derivatives and integrals (real functions) 34A08 Fractional differential equations 34G20 Nonlinear ODE in abstract spaces 45J05 Integro-ordinary differential equations
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##### References:
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