THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES∗

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗

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doi:10.1007/s10473-023-0410-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1603-1617.doi: 10.1007/s10473-023-0410-2

Shangquan BU¹, Gang CAI^2,†

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

收稿日期:2022-03-11 修回日期:2022-06-29 发布日期:2023-08-08
通讯作者: †Gang CAI, E-mail: caigang-aaaa@163.com
作者简介:Shangquan BU, E-mail: bushangquan@mail.tsinghua.edu.cn
基金资助:
* NSF of China (12171266, 12171062) and the NSF of Chongqing (CSTB2022NSCQ-JQX0004).

Shangquan BU¹, Gang CAI^2,†

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2022-03-11 Revised:2022-06-29 Published:2023-08-08
Contact: †Gang CAI, E-mail: caigang-aaaa@163.com
About author:Shangquan BU, E-mail: bushangquan@mail.tsinghua.edu.cn
Supported by:
* NSF of China (12171266, 12171062) and the NSF of Chongqing (CSTB2022NSCQ-JQX0004).

摘要： Let $X$ be a complex Banach space and let $B$ and $C$ be two closed linear operators on $X$ satisfying the condition $D(B)\subset D(C)$ , and let $d\in L^1(\mathbb{R}_+)$ and $0 \leq \beta < \alpha\leq 2$ . We characterize the well-posedness of the fractional integro-differential equations $D^\alpha u(t) + CD^\beta u(t)$ $= Bu(t) + \int_{-\infty}^t d(t-s)Bu(s){\rm d}s + f(t),\ (0\leq t\leq 2\pi)$ on periodic Lebesgue-Bochner spaces $L^p(\mathbb{T}; X)$ and periodic Besov spaces $B_{p,q}^s(\mathbb{T}; X)$ .

关键词: Lebesgue-Bochner spaces, fractional integro-differential equations, multiplier, well-posedness

Abstract: Let $X$ be a complex Banach space and let $B$ and $C$ be two closed linear operators on $X$ satisfying the condition $D(B)\subset D(C)$ , and let $d\in L^1(\mathbb{R}_+)$ and $0 \leq \beta < \alpha\leq 2$ . We characterize the well-posedness of the fractional integro-differential equations $D^\alpha u(t) + CD^\beta u(t)$ $= Bu(t) + \int_{-\infty}^t d(t-s)Bu(s){\rm d}s + f(t),\ (0\leq t\leq 2\pi)$ on periodic Lebesgue-Bochner spaces $L^p(\mathbb{T}; X)$ and periodic Besov spaces $B_{p,q}^s(\mathbb{T}; X)$ .

Key words: Lebesgue-Bochner spaces, fractional integro-differential equations, multiplier, well-posedness

Shangquan BU, Gang CAI. THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1603-1617.

Shangquan BU, Gang CAI. THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1603-1617.

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