Multi-valued nonlinear perturbations of time fractional evolution equations in Banach spaces

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• 作者：Rong-Nian Wang ; Peng-Xian Zhu ; Qing-Hua Ma
• 关键词：Fractional evolution inclusions ; Topological structure of solution set ; Invariance of reachability set
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：80
• 期：4
• 页码：1745-1759
• 全文大小：530 KB
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• 作者单位：Rong-Nian Wang (1)
  Peng-Xian Zhu (2)
  Qing-Hua Ma (1)
  
  1. Department of Applied Mathematics, Guangdong University of Foreign Studies, Guangzhou, 510420, People鈥檚 Republic of China
  2. Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, People鈥檚 Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

The paper is concerned with the fractional evolution inclusion \(^\mathrm{c}D_t^q u(t)\in Au(t)+F(t,u(t))\) in Banach spaces, where \(^\mathrm{c}D_t^q\), \(0<q<1\), is the regularized Caputo fractional derivative of order q, A generates a compact semigroup, and \(F\) is a multi-valued function with convex, closed values. Constructing a suitable directionally \(L^p\)-integrable selection from \(F\), we study the compactness and \(R_\delta \)-structure of the set of trajectories on a closed domain. Moreover, we discuss the \(R_\delta \)-structure of the set of trajectories to the control problem corresponding to the inclusion above. Finally, we apply our abstract theory to boundary value problems of fractional diffusion inclusions.