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Non-autonomous maximal regularity for fractional evolution equations

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Abstract

We consider the problem of maximal regularity for the semilinear non-autonomous fractional equations

$$\begin{aligned} B^\alpha u(t)+A(t)u(t)=F(t,u),\, t \text {-a.e}. \end{aligned}$$

Here \(B^\alpha \) denotes the Riemann–Liouville fractional derivative of order \(\alpha \in (0,1)\) w.r.t. time and the time- dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space \({\mathcal {H}}.\) We prove maximal \(L^p\)-regularity results and other regularity properties for the solution of the above equation under minimal regularity assumptions on the forms and the inhomogeneous term F.

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  1. CNRS, CPT and Institut de Mathématiques (I2M), Univ. Aix Marseille, Marseille, France

    Achache Mahdi

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Mahdi, A. Non-autonomous maximal regularity for fractional evolution equations. J. Evol. Equ. 22, 48 (2022). https://doi.org/10.1007/s00028-022-00808-4

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