Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations

This paper investigates a semilinear stochastic fractional Rayleigh-Stokes equation featuring a Riemann-Liouville fractional derivative of order α ∈ (0, 1) in time and a fractional time-integral noise.The study begins with an examination of the solution's existence, uniqueness, and regularity.The spatial discretization is then carried out using a finite element method, and the error estimate is analyzed.A convolution quadrature method generated by the backward Euler method is employed for the time discretization resulting in a fully discrete scheme.The error estimate for the fully discrete solution is considered based on the regularity of the solution, and a strong convergence rate is established.The paper concludes with numerical tests to validate the theoretical findings.