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Existence, uniqueness and regularity of the solution of the time-fractional Fokker–Planck equation with general forcing

2019
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Communications on Pure and Applied Analysis
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A time-fractional Fokker-Planck initial-boundary value problem is considered, with differential operator ut − ∇ · (∂ 1−α t κα∇u − F∂ 1−α t u), where 0 < α < 1. The forcing function F = F(t, x), which is more difficult to analyse than the case F = F(x) investigated previously by other authors. The spatial domain Ω ⊂ R d , where d ≥ 1, has a smooth boundary. Existence, uniqueness and regularity of a mild solution u is proved under the hypothesis that the initial data u 0 lies in L 2 (Ω). For 1/2

doi:10.3934/cpaa.2019124
fatcat:t6wepwrilbburjil6db2zi3c6i