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Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations. (English) Zbl 1268.34010

Summary: We are concerned with the existence and uniqueness of a weighted pseudo almost automorphic mild solution to the semilinear fractional equation: \(D^\alpha_tu(t)=Au(t)+D^{\alpha-1}_t f(t,u(t))\), \(t \in\mathbb R\), \(1<\alpha<2\) in complex Banach spaces with \(S^p\)-weighted pseudo almost automorphic coefficients, where \(A\) is a linear densely defined operator of sectorial type on a complex Banach space \(\mathbb X\). Moreover, we present an application to a fractional wave equation.

MSC:

34A08 Fractional ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
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