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The existence and exponential behavior of solutions to time fractional stochastic delay evolution inclusions with nonlinear multiplicative noise and fractional noise

  • * Corresponding author: Yejuan Wang

    * Corresponding author: Yejuan Wang

This work was supported by NSF of China (Grant Nos. 41875084, 11801452, 11571153), the Fundamental Research Funds for the Central Universities under Grants No. lzujbky-2018-ot03 and lzujbky-2018-it58, the Natural Science Basic Research Plan in Shaanxi Province of China under Grant No. 2019JQ-196, and the Doctor Fund of Northwest A & F University under Grant No. 2452018017

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  • This article is devoted to study time fractional stochastic evolution inclusions with infinite delays driven by a nonlinear multiplicative noise and a fractional Brownian motion with Hurst parameter $ H\in(\frac{1}{2},1) $. First of all, we investigate the local and global existence of mild solutions to such evolution inclusions by using the fractional resolvent operator theory and some new results on the measure of noncompactness for the stochastic integral term. Further, we prove that every mild solution decays exponentially to zero in the sense of mean-square topology.

    Mathematics Subject Classification: Primary: 34A08, 34K09, 34K50, 35K58.


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