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doi: 10.3934/dcdsb.2021267
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Dynamics of fractional nonclassical diffusion equations with delay driven by additive noise on $ \mathbb{R}^n $

1. 

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

2. 

Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

* Corresponding author: Pengyu Chen

Received  June 2021 Revised  September 2021 Early access November 2021

Fund Project: Research supported by National Natural Science Foundations of China (No. 12061063), Natural Science Foundation of Gansu Province (No. 21JR7RA159 and No. 20JR5RA522), Project of NWNU-LKQN2019-3 and Project of NWNU-LKQN2019-13

In this paper, we study the asymptotic behavior of solutions of fractional nonclassical diffusion equations with delay driven by additive noise defined on unbounded domains. We first prove the uniform compactness of pullback random attractors of the equation with respect to noise intensity and time delay, and then establish the upper semi-continuity of these attractors as either noise intensity or time delay approaches zero.

Citation: Pengyu Chen, Bixiang Wang, Xuping Zhang. Dynamics of fractional nonclassical diffusion equations with delay driven by additive noise on $ \mathbb{R}^n $. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021267
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References:
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[13]

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[14]

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[18]

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T. Caraballo, A. M. Márquez-Durán and F. Rivero, Well-posedness and asymptotic behavior of a nonclassical nonautonomous diffusion equation with delay, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 25 (2015), 1540021, 11 pp. doi: 10.1142/S0218127415400210.  Google Scholar

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