Abstract
We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces \(B_{p,q}^s\left( {T;X} \right)\) (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ and 0 < β < α are fixed. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for Lp-well-posedness and \(B_{p,q}^s\)-well-posedness of above equation.
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Bu, S., Cai, G. Well-Posedness of Fractional Degenerate Differential Equations in Banach Spaces. FCAA 22, 379–395 (2019). https://doi.org/10.1515/fca-2019-0023
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DOI: https://doi.org/10.1515/fca-2019-0023