In this paper, we consider an initial-boundary value problem for a stochastic non-linear heat equation with Riemann-Liouville spacefractional derivative and white noise on the half-line. We construct the integral representation of the solution and prove existence and uniqueness. Moreover, we adapt stochastic integration methods to approximate the solutions

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In this work, we present four results for the Laplace inverse transform of functions that involve the nth root of a product of linear factors. In order to find the Laplace inverse transform, we considered a branch cut for the nth root and a region of suitable integration, to avoid the branching points. Due to that, the solution is in terms of integrals, we easily approach this solution for some specific parameters.