[1] Abidin M, Chen J. Global well-posedness for fractional Navier-Stokes equations in variable exponent Fourier-Besov-Morrey spaces. Acta Math Sci, 2021, 41(1):164-176
[2] Applebaum D. Lévy Processes and Stochastic Calculus. Cambridge University Press, 2009
[3] Arnold L. Random Dynamical Systems. Springer, 2013
[4] Bai L, Cheng X, Duan J, Yang M. Slow manifold for a nonlocal stochastic evolutionary system with fast and slow components. J Differ Equ, 2017, 263(8):4870-4893
[5] Bates P, Lu K, Zeng C. Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space. American Mathematical Society, 1998
[6] Bucur C, Valdinoci E. Nonlocal Diffusion and Applications. Springer, 2016
[7] Caffarelli L, Vasseur A. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann Math, 2010, 171(3):1903-1930
[8] Caraballo T, Chueshov I, Langa J. Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations. Nonlinearity, 2005, 18(2):747-767
[9] Castaing C, Valadier M. Convex Analysis and Measurable Multifunctions. Berlin, Heiddelberg, New York:Springer-Verlag, 1977
[10] Chen G, Duan J, Zhang J. Slow foliation of a slow-fast stochastic evolutionary system. J Funct Anal, 2014267(8):2663-2697
[11] Chicone C, Latushkin Y. Center manifolds for infinite dimensional nonautonomous differential equations. J Differ Equ, 1997, 141(2):356-399
[12] Chow S, Lu K. Invariant manifolds for flows in banach spaces. J Differ Equ, 1988, 74(2):285-317
[13] Chow S, Lu K, Lin X. Smooth foliations for flows in banach space. J Differ Equ, 1991, 94(1):266-291
[14] Cronin J. Mathematical Aspects of Hodgkin-Huxley Neural Theory. Cambridge University Press, 1987
[15] Prato D, Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge University Press, 2014
[16] Duan J. An Introduction to Stochastic Dynamics. Volume 51. Cambridge University Press, 2015
[17] Duan J, Lu K, Schmalfuß B. Smooth stable and unstable manifolds for stochastic evolutionary equations. J Differ Equ, 2004, 16(4):949-972
[18] Duan J, Lu K, SchmalfußB, et al. Invariant manifolds for stochastic partial differential equations. Ann Probab, 2003, 31(4):2109-2135
[19] Duan J, Wang W. Effective Dynamics of Stochastic Partial Differential Equations. New York:Elsevier, 2014
[20] Evans L. Partial Differential Equations. American Mathematical Society, 2015
[21] FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J, 1961, 1(6):445-466
[22] Fu H, Liu X, Duan J. Slow manifolds for multi-time-scale stochastic evolutionary systems. Comm Math Sci, 2013,11(1):141-162
[23] Hadamard J. Sur l'itération et les solutions asymptotiques des équations différentielles. Bull Soc Math France, 1901, 29:224-228
[24] Henry D. Geometric Theory of Semilinear Parabolic Equations. Springer, 1981
[25] Kwásnicki M. Eigenvalues of the fractional Laplace operator in the interval. J Funct Anal, 2012, 262(5):2379-2402
[26] Li G, Tao Y. The existence of a nontrivial weak solution to a double critical problem involving a fractional Laplacian in $\mathbb{R}^{N}$ with a Hardy term. Acta Math Sci, 2020, 40(6):1808-1830
[27] Liu X. Symmetry of positive solutions for the fractional Hartree equation. Acta Math Sci, 2019, 39(6):1508-1516
[28] Meerschaert M, Sikorskii A. Stochastic Models for Fractional Calculus. Walter de Gruyter, 2012
[29] Metzler R, Klafter J. The restaurant at the end of the random walk:recent developments in the description of anomalous transport by fractional dynamics. J Phys A-Math Gen, 2004, 37(31):R161-R208
[30] Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc IRE, 1962, 50(10):2061-2070
[31] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, 2012
[32] Ren J, Duan J, Jones C. Approximation of random slow manifolds and settling of inertial particles under uncertainty. J Dyn Differ Equ, 2015, 27(3/4):961-979
[33] Ren J, Duan J, Wang X. A parameter estimation method based on random slow manifolds. Appl Math Model, 2015, 39(13):3721-3732
[34] Ruelle D. Characteristic exponents and invariant manifolds in hilbert space. Ann Math, 1982, 115(2):243-290
[35] Schmalfuß B. A random fixed point theorem and the random graph transformation. J Math Anal Appl, 1998, 225(1):91-113
[36] Schmalfuß B, Schneider K. Invariant manifolds for random dynamical systems with slow and fast variables. J Dyn Differ Equ, 2008, 20(1):133-164
[37] Wang W, Roberts A. Slow manifold and averaging for slow-fast stochastic differential system. J Math Anal Appl, 2013, 398(2):822-839
[38] Wanner T. Linearization of random dynamical systems. Dynamics reported, 1995, 4(1):203-269
[39] Yan X, He J, Duan J. Approximation of the inertial manifold for a nonlocal dynamical system. arXiv preprint arXiv:1403.0165, 2014
[40] Youssfi A, Mahmoud G. On singular equations involving fractional Laplacian. Acta Math Sci, 2020, 40(5):1289-1315 |