APPROXIMATE CONTROLLABILITY OF SOBOLEV TYPE FRACTIONAL EVOLUTION EQUATIONS OF ORDER <i>α</i> ∈ (1, 2) VIA RESOLVENT OPERATORS

He Yang

doi:10.11948/20210086

2021 Volume 11 Issue 6

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He Yang. APPROXIMATE CONTROLLABILITY OF SOBOLEV TYPE FRACTIONAL EVOLUTION EQUATIONS OF ORDER α ∈ (1, 2) VIA RESOLVENT OPERATORS[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2981-3000. doi: 10.11948/20210086

Citation:

He Yang. APPROXIMATE CONTROLLABILITY OF SOBOLEV TYPE FRACTIONAL EVOLUTION EQUATIONS OF ORDER α ∈ (1, 2) VIA RESOLVENT OPERATORS[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2981-3000. doi: 10.11948/20210086

APPROXIMATE CONTROLLABILITY OF SOBOLEV TYPE FRACTIONAL EVOLUTION EQUATIONS OF ORDER α ∈ (1, 2) VIA RESOLVENT OPERATORS

He Yang^,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou Gansu 730070, China

Corresponding author: Email: yanghe256@163.com(H. Yang)
Fund Project: The author was supported by National Natural Science Foundation of China (No. 12061062)

Abstract

Abstract

In this paper, the existence and approximate controllability of mild solutions for $ \alpha\in(1,2) $-order fractional evolution equations of Sobolev type are investigated in abstract spaces. Firstly, we introduce a new concept of mild solution of the concerned problem. Then by using fixed point theorems and the theory of resolvent operator, some existence results are obtained. At last, the approximate controllability of the $ \alpha\in(1,2) $-order fractional evolution equation is proved without assuming the approximate controllability of corresponding linear problem. An example is presented in the last section to illustrate the obtained abstract results.
- Approximate controllability /
- fractional evolution equations /
- fractional resolvent family /
- existence /
- nonlocal condition
MSC: 47A10, 93B05

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