Non autonomous maximal regularity for the fractional evolution equations
Résumé
We consider the problem of maximal regularity for the semilinear non-autonomous fractional equations B α u(t) + A(t)u(t) = F (t, u), t-a.e. Here, B α denotes the Riemann-Liouville fractional derivative of order α ∈ (0, 1) w.r.t. time and the time dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space H. We prove maximal L p-regularity results and other regularity properties for the solutions of the above equation under minimal regularity assumptions on the forms and the inhomogeneous term F.
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