On the controllability results of semilinear delayed evolution systems involving fractional derivatives in Banach spaces

Lijuan Qin; Lijuan Qin

doi:10.3934/math.2024875

AIMS Mathematics

2024, Volume 9, Issue 7: 17971-17983. doi: 10.3934/math.2024875

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Research article

On the controllability results of semilinear delayed evolution systems involving fractional derivatives in Banach spaces

Lijuan Qin ^,

College of Science, Gansu Agricultural University, Lanzhou Gansu 730070, China

Received: 02 March 2024 Revised: 04 May 2024 Accepted: 06 May 2024 Published: 27 May 2024
MSC : 34K30, 34K35, 93C25

The paper investigated the exact controllability of delayed fractional evolution systems of order $ \alpha\in (1, 2) $ in abstract spaces. At first, the exact controllability result is obtained when the nonlinear term $ f $ is locally Lipschitz continuous. Then, the certain compactness conditions and the measure of noncompactness conditions were applied to demonstrate the exact controllability of the concerned problem. The discussion was based on the fixed point theorems and the cosine family theory.
- the cosine family theory,
- exact controllability,
- fractional evolution equations,
- fixed point theorem
Citation: Lijuan Qin. On the controllability results of semilinear delayed evolution systems involving fractional derivatives in Banach spaces[J]. AIMS Mathematics, 2024, 9(7): 17971-17983. doi: 10.3934/math.2024875

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Abstract

The paper investigated the exact controllability of delayed fractional evolution systems of order $ \alpha\in (1, 2) $ in abstract spaces. At first, the exact controllability result is obtained when the nonlinear term $ f $ is locally Lipschitz continuous. Then, the certain compactness conditions and the measure of noncompactness conditions were applied to demonstrate the exact controllability of the concerned problem. The discussion was based on the fixed point theorems and the cosine family theory.

References

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