Weighted pseudo almost automorphic classical solutions and optimal mild solutions for fractional differential equations and application in fractional reaction–diffusion equations
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- 作者：Junfei Cao (1)
Zaitang Huang (2)
Caibin Zeng (3) - 关键词：Optimal mild solution ; Weighted pseudo ; almost automorphic classical solution ; Fractional differential equation ; Fractional reaction–diffusion equation ; Existence and uniqueness
- 刊名：Journal of Mathematical Chemistry
- 出版年：2014
- 出版时间：August 2014
- 年：2014
- 卷：52
- 期：7
- 页码：1984-2012
- 全文大小：273 KB
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Zaitang Huang (2)
Caibin Zeng (3)
1. Department of Mathematics, Guangdong University of Education, Guangzhou, 510310, People’s Republic of China
2. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, 530023, People’s Republic of China
3. Department of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China - ISSN：1572-8897
文摘
In this paper, we are concerned with a class of fractional differential equations given by $$\begin{aligned} \hbox {D}_{t}^{\alpha }x(t)=Ax(t)+f(t,x(t)). \end{aligned}$$ Our main results concern the existence, uniqueness of weighted pseudo-almost automorphic classical solutions and optimal mild solutions. Moreover, as example and applications, we study the weighted pseudo-almost automorphic classical solutions and optimal mild solutions for a fractional reaction–diffusion equation to illustrate the practical usefulness of the analytical results that we establish in the paper.