Well‐posedness of degenerate fractional differential equations with finite delay in complex Banach spaces

Shangquan Bu and Gang Cai

Mathematische Nachrichten, 2024, vol. 297, issue 4, 1535-1549

Abstract: We study the well‐posedness of the degenerate fractional differential equations with finite delay: Dα(Mu)(t)+cDβ(Mu)(t)$D^\alpha (Mu)(t) + cD^\beta (Mu)(t)$ =Au(t)+Fut+f(t),(0≤t≤2π)$= Au(t) + Fu_t + f(t),(0\le t\le 2\pi )$ on Lebesgue–Bochner spaces Lp(T;X)$L^p(\mathbb {T}; X)$ and periodic Besov spaces Bp,qs(T;X)$B_{p,q}^s(\mathbb {T}; X)$, where A$A$ and M$M$ are closed linear operators in a complex Banach space X$X$ satisfying D(A)⊂D(M)$D(A)\subset D(M)$, c∈C$c\in \mathbb {C}$ and 0

Date: 2024
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