APPROXIMATION OF FRACTIONAL RESOLVENTS AND APPLICATIONS TO TIME OPTIMAL CONTROL PROBLEMS

Shouguo Zhu; Gang Li

doi:10.11948/20190056

2020 Volume 10 Issue 2

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Shouguo Zhu, Gang Li. APPROXIMATION OF FRACTIONAL RESOLVENTS AND APPLICATIONS TO TIME OPTIMAL CONTROL PROBLEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 649-666. doi: 10.11948/20190056

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Shouguo Zhu, Gang Li. APPROXIMATION OF FRACTIONAL RESOLVENTS AND APPLICATIONS TO TIME OPTIMAL CONTROL PROBLEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 649-666. doi: 10.11948/20190056

APPROXIMATION OF FRACTIONAL RESOLVENTS AND APPLICATIONS TO TIME OPTIMAL CONTROL PROBLEMS

Shouguo Zhu^1,2, ,,
Gang Li²

1.
Wuxi Institute of Technology, Wuxi 214121, China
2.
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Corresponding author: the corresponding author. Email address: sgzhu2015@163.com (S. Zhu)
Fund Project: The authors were supported by the NSF of China (Nos. 11771378, 11871064) and the NSF of the JiangSu Higher Education Institutions (18KJB110019)

Abstract

Abstract

We investigate the approximation of fractional resolvents, extending and improving some corresponding results on semigroups and resolvents. As applications, we utilize the approach of Meyer approximation to analyze the time optimal control problem of a Riemann-Liouville fractional system without Lipschitz continuity. A fractional diffusion model is also presented to confirm our theoretical findings.
- Resolvent /
- Riemann-Liouville fractional derivatives /
- time optimal controls /
- Meyer approximation
MSC: 47A10, 49J15, 93C25

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