Abstract
In this work, we consider an initial boundary-value problem for a stochastic evolution equation with fractional Laplacian and white noise on the first quadrant. To construct the integral representation of solutions we adapt the main ideas of the Fokas method and by using Picard scheme we prove its existence and uniqueness. Moreover, Monte Carlo methods are implemented to find numerical solutions for particular examples.
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Sanchez-Ortiz, J., Ariza-Hernandez, F.J., Arciga-Alejandre, M.P. et al. Stochastic Diffusion Equation with Fractional Laplacian on the First Quadrant. FCAA 22, 795–806 (2019). https://doi.org/10.1515/fca-2019-0043
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DOI: https://doi.org/10.1515/fca-2019-0043