References
- Dong J, Xu M. Space-time fractional Schrödinger equation with time-independent potentials. J Math Anal Appl. 2008;344:1005–1017.
- Guan Q, Ma Z. Boundary problems for fractional laplacians. Stoch Dyn. 2005;5:385–424.
- Lan Y, Shu J. Fractal dimension of random attractors for non-autonomous fractional stochastic Ginzburg–Landau equations with multiplicative noise. Dyn Syst. 2019;34:274–300.
- Lu H, Bates PW, Lu S, et al. Dynamics of the 3D fractional Ginzburg–Landau equation with multiplicative noise on a unbounded domain. Comm Math Sci. 2016;14:273–295.
- Pu X, Guo B. Well-posedness and dynamics for the fractional Ginzburg–Laudau equation. Appl Anal. 2013;92:318–334.
- Shu J, Li P, Zhang J, et al. Random attractors for the stochastic coupled fractional Ginzburg–Landau equation with additive noise. J Math Phys. 2015;56:102702.
- Guo B, Zeng M. Soltuions for the fractional Landau-Lifshitz equation. J Math Anal Appl. 2010;361:131–138.
- Gu A, Li D, Wang B, et al. Regularity of random attractors for fractional stochastic reaction–diffusion equations on Rn. J Differ Equ. 2018;264:7094–7137.
- Wang B. Asymptotic behavior of non-autonomous fractional stochastic reaction–diffusion equations. Nonlinear Anal. 2017;158:60–82.
- Zhou S, Tian Y, Wang W. Fractal dimension of random attractors for stochastic non-autonomous reaction–diffusion equations. Appl Math Comput. 2016;276:80–95.
- Servadei R, Valdinoci E. On the spectrum of two different fractional operators. Proc Roy Soc Edinburgh Sect A. 2014;144:831–855.
- Cao D, Sun C, Yang M. Dynamics for a stochastic reaction–diffusion equation with additive noise. J Differ Equ. 2015;259:838–872.
- Caraballo T, Langa J, Robinson JC. Staility and random attractors for a reaction–diffusion equation with multiplicative noise. Discrete Contin Dyn Syst. 2000;6:875–892.
- Crauel H, Flandoli F. Attractors for random dynamical systems. Probab Theory Related Fields. 1994;100:365–393.
- Debussche A. Hausdorff dimension of a random invariant set. J Math Pures Appl. 1998;77:967–988.
- Guo C, Shu J, Wang X. Fractal dimension of random attractors for non-autonomous fractional stochastic Ginzburg–Landau equations. Acta Math Sin (Engl Ser). 2020;36(3):318–336.
- Li D, Wang B, Wang X. Limiting behavior of non-autonomous stochastic reaction–diffusion equations on thin domains. J Differ Equ. 2017;262:1575–1602.
- Li J, Li Y, Wang B. Random attractors of reaction–diffusion equations with multiplicative noise in Lp. Appl Math Comput. 2010;215:3399–3407.
- Li Y, Guo B. Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction–diffusion equations. J Differ Equ. 2008;245:1775–1800.
- Ma D, Shu J, Qin L. Wong-Zakai approximations and asymptotic behavior of stochastic Ginzburg–Landau equations. Discrete Contin Dyn Syst Ser B. 2020. doi:https://doi.org/10.3934/dcdsb.2020100.
- Wang G, Tang Y. Random attractors for stochastic reaction–diffusion equations with multiplicative noise in H01. Math Nachr. 2014;287:1774–1791.
- Zhou S, Zhao M. Fractal dimension of random attractor for stochastic damped wave equation with multiplicative noise. Discrete Contin Dyn Syst. 2017;263:2247–2279.
- Bates PW, Lu K, Wang B. Random attractors for stochastic reaction–diffusion equations on unbounded domains. J Differ Equ. 2009;246:845–869.
- Chueshov ID. Gevrey ragularity of random attractors for stochastic reaction–diffusion equations. Random Oper Stoch Equ. 2000;8:143–162.
- Chepyzhov VV, Efendiev MA. Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: an example. Comm Pure Appl Math. 2000;53:647–665.
- Wang B. Attractors for reaction–diffusion equations in unbounded domains. Phys D. 1999;128:41–52.
- Wang B. Upper semicontinuity of random attractors for non-compact random systems. J Differ Equ. 2009;139:1–18.
- Wang B. Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems. J. Differ Equ. 2012;253:1544–1583.
- Wang X, Lu K, Wang B. Wong-Zakai approximations and attractors for stochastic reaction–diffusion equations on unbounded domains. J. Differ Equ. 2018;264:378–424.
- Wang Z, Zhou S. Random attractor for stochastic reaction–diffusion equation with multiplicative noise on unbounded domains. J Math Anal Appl. 2011;384:160–172.
- Zhao W, Li Y. (L2,Lp)-random attractors for stochastic reaction–diffusion equation on unbounded domains. Nonlinear Anal. 2012;75:485–502.
- Zhou S. Random exponential attractor for stochastic reaction–diffusion equation with multiplicative noise in R3. J Differ Equ. 2017;263:6347–6383.
- Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. Strong convergence of trajectory attractors for reaction–diffusion systems with random rapidly oscillating terms. Commun Pure Appl Anal. 2020;19(5):2419–2443.
- Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. Weak convergence of attractors of reaction–diffusion systems with randomly oscillating coefficients. Appl Anal. 2019;98(1-2):256–271.
- Bekmaganbetov KA, Chechkin GA, Chepyzhov VV, et al. Homogenization of trajectory attractors of 3D Navier–Stokes system with randomly oscillating force. Discrete Contin Dyn Syst. 2017;37(5):2375–2393.
- Chechkin GA, Chepyzhov VV, Pankratov LS. Homogenization of trajectory attractors of Ginzburg–Landau equations with randomly oscillating terms. Discrete Contin Dyn Syst Ser B. 2018;23(3):1133–1154.
- Bai Q, Shu J, Li L, et al. Dynamical behavior of non-autonomous fractional stochastic reaction–diffusion equations. J Math Anal Appl. 2020;485:123833.
- Lan Y, Shu J. Dynamics of non-autonomous fractional stochastic Ginzburg–Landau equations with multiplicative noise. Commun Pure Appl Anal. 2019;18:2409–2431.
- Li L, Shu J, Bai Q, et al. Asymptotic behavior of fractional stochastic heat equations in materials with memory. Appl Anal. 2019. doi:https://doi.org/10.1080/00036811.2019.1597057.
- Liu L, Fu X. Dynamics of a stochastic fractional reaction–diffusion equation. Taiwanese J Math. 2018;22:95–124.
- Lu H, Bates PW, Xin J, et al. Asymptotic behavior of stochastic fractional power dissipative equations on Rn. Nonlinear Anal. 2015;128:176–198.
- Wang B. Random attractors for non-autonomous stochastic wave equations with multiplicative noise. Discrete Contin Dyn Syst. 2014;34:269–300.
- Crauel H, Debussche A, Flandoli F. Random attractors. J Dynam Differ Equ. 1997;9:307–341.
- Flandoli F, Schmalfuss B. Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise. Stoch Stoch Rep. 1996;59:21–45.
- Schmalfuss B. Backward cocycle and atttractors of stochastic differential equations. In: Reitmann V, Riedrich T, Koksch N, editors. International semilar on applied mathematics-nonlinear dynamics: attractor approximation and global behavior. Dresden: Technische Universität; 1992. p. 185–192.
- Arnold LRandom dynamical systems. Berlin: Springer; 1998.
- Caraballo T, Kloeden PE, Schmalfuß B. Exponentially stable stationary solutions for stochastic evolution equations and their perturbation. Appl Math Optim. 2004;50:183–207.
- Debussche A. On the finite dimensionality of random attractors. Stoch Anal Appl. 1997;15:473–491.
- Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573.
- Tang B. Regularity of random attractors for stochastic reaction–diffusion equations on unbounded domains. Stoch Dyn. 2016;16:1650006.
- Morosi C, Pizzocchero L. On the constants for some fractional Gagliardo-Nirenberg and Sobolev inequalities. Expo Math. 2018;36:32–77.