数学
欧米茄
巴拿赫空间
类型(生物学)
背景(考古学)
振荡(细胞信号)
分数阶微积分
空格(标点符号)
放松(心理学)
数学分析
数学物理
纯数学
物理
量子力学
心理学
哲学
古生物学
生物
社会心理学
遗传学
语言学
生态学
作者
Darin Brindle,Gaston M. N’Guérékata
标识
DOI:10.58997/ejde.2020.30
摘要
This article concerns the existence of mild solutions to the semilinear fractional differential equation $$ D_t^\alpha u(t)=Au(t)+D_t^{\alpha-1} f(t,u(t)),\quad t\geq 0 $$ with nonlocal conditions \(u(0)=u_0 + g(u)\) where \(D_t^\alpha(\cdot)\) (\(1< \alpha < 2\)) is the Riemann-Liouville derivative, \(A: D(A) \subset X \to X\) is a linear densely defined operator of sectorial type on a complex Banach space \(X\), \(f:\mathbb{R}^+\times X\to X\) is S-asymptotically \(\omega\)-periodic with respect to the first variable. We use the Krsnoselskii's theorem to prove our main theorem. The results obtained are new even in the context of asymptotically \(\omega\)-periodic functions. An application to fractional relaxation-oscillation equations is given.For more information see https://ejde.math.txstate.edu/Volumes/2020/30/abstr.html
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