Framework for Solving Fractional Stochastic Integral-Differential Equations

TL;DR

This paper presents a new framework using operational matrices and shifted Legendre polynomials to numerically solve fractional stochastic differential equations, enabling better analysis of uncertain dynamic systems.

Contribution

It introduces a novel operational matrix approach based on 2D shifted Legendre polynomials for solving fractional stochastic differential equations.

Findings

Efficient numerical solutions for fsDEs achieved.

Operational matrices simplify complex fractional stochastic systems.

Framework applicable to various uncertain dynamic models.

Abstract

This article introduces a framework for measuring the uncertain behaviour of a changing system in terms of the solution of a class of fractional stochastic differential equations (fsDEs). This is accomplished via operational matrices based on 2-dimensional shifted Legendre polynomials. By using operational matrices, an fsDE is converted into a matrix form and the numerical solution of the represented motion system is then found.