Analysis and Numerical Solutions for Fractional Stochastic Evolution Equations With Almost Sectorial Operators

Abstract

Fractional stochastic evolution equations often arise in theory and applications. Finding exact solutions of such equations is impossible in most cases. In this paper, our main goal is to establish the existence and uniqueness of mild solutions of the equations, and give a numerical method for approximating such mild solutions. The numerical method is based on a combination of subspaces decomposition technique and waveform relaxation method, which is called a frequency decomposition waveform relaxation method. Moreover, the convergence of the frequency decomposition waveform relaxation method is discussed in detail. Finally, several illustrative examples are presented to confirm the validity and applicability of the proposed numerical method.