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Zbl 1189.34079
Chen, Anping; Chen, Fulai; Deng, Siqing
On almost automorphic mild solutions for fractional semilinear initial value problems. (English)
[J] Comput. Math. Appl. 59, No. 3, 1318-1325 (2010). ISSN 0898-1221

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 2000:: *34C27 Almost periodic solutions of ODE
26A33 Fractional derivatives and integrals (real functions)
34A08
34G20 Nonlinear ODE in abstract spaces
45J05 Integro-ordinary differential equations

Keywords: fractional differential equation; almost automorphic function; mild solution

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