PARTIAL-APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL BACKWARD EVOLUTION SYSTEMS

Shouguo Zhu; Gang Li

doi:10.11948/20200131

2022 Volume 12 Issue 4

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Shouguo Zhu, Gang Li. PARTIAL-APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL BACKWARD EVOLUTION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1259-1276. doi: 10.11948/20200131

Citation:

Shouguo Zhu, Gang Li. PARTIAL-APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL BACKWARD EVOLUTION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1259-1276. doi: 10.11948/20200131

PARTIAL-APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL BACKWARD EVOLUTION SYSTEMS

Shouguo Zhu^1, ,,
Gang Li²

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

Corresponding author: Email address: sgzhu2015@163.com(S. Zhu)
Fund Project: The authors were supported by the NSF of China (Nos. 11771378, 11871064), the NSF of the JiangSu Higher Education Institutions (18KJB110019) and the Doctor Research Foundation (BT2019-03)

Abstract

Abstract

This paper addresses a Hilfer fractional backward evolution model. We first develop the dual theory of resolvent. Then, we motivate the transformation technique and the resolvent method to formulate a suitable concept of mild solutions to this model. In addition, with the help of the dual properties of resolvent, we employ the variational technique to treat the partial-approximate controllability problem of the system. We end up analyzing a Hilfer fractional diffusion backward control system by using our theoretical results.
- Hilfer fractional evolution equations /
- backward systems /
- resolvent /
- partial-approximate controllability
MSC: 34K37, 47A10, 93B05

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References

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