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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 Dαx(t)=Ax(t)+f(t,x(t)), 0<α<1, considered in a Banach space X, where A is a linear operator of sectorial type ω<0. Some sufficient conditions are given for the existence, uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation.
MSC:
34C27Almost and pseudo-almost periodic solutions of ODE
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
34G20Nonlinear ODE in abstract spaces
45J05Integro-ordinary differential equations
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