A Neumann problem for a diffusion equation with n-dimensional fractional Laplacian

Abstract

We study an initial-boundary value problem for a n-dimensional stochastic diffusion equation with fractional Laplacian on $\mathbb{R}_{+}^{n}$ R + n . In order to prove existence and uniqueness, we generalize the Fokas method to construct the Green function for the associated linear problem and then we apply a fixed point argument. Also, we present an example where the explicit solutions are given.