## 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:

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

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