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Well-posednss and Convergence for Time-Space Fractional Stochastic Schrodinger-BBM Equations
Shang Wu,Jianhua Huang,Yuhong Li
Keywords:Schrodinger-BBM Equation; Caputo fractional derivative; Mild solution; Galerkin finite element method.
Abstract:
      In this paper, the Banach fixed point theorem combined with Mittag-Leffler functions has been used to obtain the existence and uniqueness of global mild solution for a kind of time-space fractional stochastic Schr\"odinger-BBM equation driven by Gaussian noise. The spatial-temporal regularity of the nonlocal stochastic convolution are established. The convergence and numerical simulation are provided by the Galerkin finite element method as well.