论文信息 - Time-space fractional stochastic Ginzburg-Landau equation driven by Gaussian white noise

Time-space fractional stochastic Ginzburg-Landau equation driven by Gaussian white noise

ABSTRACT The current article is devoted to the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein-Ulenbeck equations. The dependence of the order of time-fractional derivative, the order of the space-fractional derivative, and the regularity of the initial data are revealed. The global existence and uniqueness of the mild solutions for time-space fractional complex Ginzburg-Landau equation driven by Gaussian white noise are established.

[1] T. Kurtz,et al. Stochastic equations in infinite dimensions , 2006 .

[2] Yong Zhou,et al. Weak solutions of the time-fractional Navier-Stokes equations and optimal control , 2017, Comput. Math. Appl..

[3] Zhong Shou-ming,et al. A Generalized Gronwall Inequality and Its Application in a Fractional Differential Equation , 2012 .

[4] Jean Leray,et al. Sur le mouvement d'un liquide visqueux emplissant l'espace , 1934 .

[5] M. Shinbrot. Fractional derivatives of solutions of the Navier-Stokes equations , 1971 .

[6] Gabriela Planas,et al. Mild solutions to the time fractional Navier-Stokes equations in R-N , 2015 .

[7] Xueke Pu,et al. Fractional Partial Differential Equations and their Numerical Solutions , 2015 .

[8] P. Kloeden,et al. Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative , 2016 .

[9] Yong Zhou,et al. On the time-fractional Navier-Stokes equations , 2017, Comput. Math. Appl..

[10] Yong-sheng Ding,et al. A generalized Gronwall inequality and its application to a fractional differential equation , 2007 .