Weak stability for integro-differential inclusions of diffusion-wave type involving infinite delays

Nguyen, Thanh-Anh; Tran, Dinh-Ke; Nguyen, Nhu-Quan

doi:10.3934/dcdsb.2016114

Cited by 15 publications

(1 citation statement)

References 21 publications

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“…Fractional partial differential equations were investigated in recent decades, see, e.g., [2,3,9,10,12,20,33,40] and the references therein. The cauchy problem associated with integro-differential inclusions of diffusion-wave type involving infinite delays has been studied in [31]. Fractional integro-differential inclusions with state-dependent delay have been considered in [5] and [41].…”

Section: Yajing LI and Yejuan Wangmentioning

confidence: 99%

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

Wang¹

2020

Discrete &Amp; Continuous Dynamical Systems - B

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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 ∈ ( 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.

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Section: Yajing LI and Yejuan Wangmentioning

confidence: 99%

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

Wang¹

2020

Discrete &Amp; Continuous Dynamical Systems - B

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On temporal regularity and polynomial decay of solutions for a class of nonlinear time‐delayed fractional reaction–diffusion equations

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Van Tuan

2024

Mathematische Nachrichten

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This paper is devoted to analyzing the regularity in time and polynomial decay of solutions for a class of fractional reaction–diffusion equations (FrRDEs) involving delays and nonlinear perturbations in a bounded domain of . By establishing some regularity estimates in both time and space variables of the resolvent operator, we present results on the Hölder and ‐regularity in time of solutions for both time‐delayed linear and semilinear FrRDEs. Based on the aforementioned results, we study the existence, uniqueness, and regularity of solutions to an identification problem subjected to the delay FrRDE and the additional observations given at final time. Furthermore, under quite reasonable assumptions on nonlinear perturbations and the technique of measure of noncompactness, the existence of decay solutions with polynomial rates for the problem under consideration is shown.

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Dissipativity and stability for semilinear anomalous diffusion equations involving delays

Thuy

2020

Math Methods in App Sciences

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Weak stability for integro-differential inclusions of diffusion-wave type involving infinite delays

Cited by 15 publications

References 21 publications

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

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

On temporal regularity and polynomial decay of solutions for a class of nonlinear time‐delayed fractional reaction–diffusion equations

Dissipativity and stability for semilinear anomalous diffusion equations involving delays

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