EXISTENCE AND APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL EVOLUTION EQUATIONS IN BANACH SPACES

Haide Gou; Yongxiang Li

doi:10.11948/20210053

2021 Volume 11 Issue 6

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Haide Gou, Yongxiang Li. EXISTENCE AND APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL EVOLUTION EQUATIONS IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2895-2920. doi: 10.11948/20210053

Citation:

Haide Gou, Yongxiang Li. EXISTENCE AND APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL EVOLUTION EQUATIONS IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2895-2920. doi: 10.11948/20210053

EXISTENCE AND APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL EVOLUTION EQUATIONS IN BANACH SPACES

Haide Gou^1, ,,
Yongxiang Li^1,

1.
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

Author Bio: Email address: liyxnwnu@163.com(Y. Li)
Corresponding author: Email address: 842204214@qq.com(H. Gou)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061062, 11661071)

Abstract

Abstract

This paper is concerned with the existence of mild solutions as well as approximate controllability for Hilfer fractional evolution equations in Banach spaces. Firstly, we give an appropriate definition of mild solutions for this type of fractional equations. The definition of mild solutions for studied problem was given based on a cosine family generated by the operator A and probability density function. Secondly, we discuss the existence results of the mild solutions for our concerned problem under the case sine family is compact. Moreover, we establish the approximate controllability when the corresponding linear system is approximately controllable. At last, as an application, two examples are presented to illustrate the abstract results.
- Hilfer fractional evolution equations /
- mild solution /
- approximate controllability /
- cosine family
MSC: 34K30, 34K45, 93B05, 26A33

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References

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