On The L{2}-Solutions of Stochastic Fractional Partial Differential Equations; Existence, Uniqueness and Equivalence of Solutions

TL;DR

This paper establishes the existence, uniqueness, and equivalence of L2-solutions for stochastic fractional PDEs in one dimension, using Fourier transform methods that accommodate random diffusion coefficients.

Contribution

It provides new proofs for existence and uniqueness of solutions and demonstrates the equivalence of different solution notions for stochastic fractional PDEs.

Findings

Proves existence and uniqueness of L2-solutions.

Shows equivalence of solution concepts.

Applies Fourier transform to stochastic fractional PDEs.

Abstract

The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The Fourier transform is used to give meaning to SFPDEs. This method is valid also when the diffusion coefficient is random.