Stochastic partial differential equations driven by space-time fractional noises

TL;DR

This paper investigates a class of stochastic partial differential equations driven by space-time fractional noises, introducing a method that involves analyzing nonlocal SPDEs and demonstrating their convergence to solve the original equations.

Contribution

The paper presents a novel approach by connecting nonlocal SPDEs with space-time fractional noise-driven equations through convergence analysis.

Findings

Established convergence of nonlocal SPDE solutions to the fractional noise-driven SPDEs.

Provided a new framework for solving SPDEs with fractional space-time noise.

Enhanced understanding of the behavior of solutions under fractional noise conditions.

Abstract

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these equations and the limit gives the solution to the SPDE.