Analysis and numerical solutions for fractional stochastic evolution equations with almost sectorial operators

[+] Author and Article Information
Xiao-Li Ding

Department of Mathematics, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China

Juan J. Nieto

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

1Corresponding author.

ASME doi:10.1115/1.4043725 History: Received January 27, 2019; Revised April 30, 2019


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.

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