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Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations. (English) Zbl 1248.34004
Summary: We study the existence and uniqueness of a weighted pseudo-almost periodic (mild) solution to the semilinear fractional equation $$\partial ^{\alpha}_t u = Au + \partial ^{\alpha - 1}_t f(\cdot, u), 1< \alpha <2,$$ where $A$ is a linear operator of sectorial negative type. This article also deals with the existence of these types of solutions to abstract partial evolution equations.

MSC:
34A08Fractional differential equations
34G20Nonlinear ODE in abstract spaces
34C27Almost and pseudo-almost periodic solutions of ODE
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