Novel Numerical Solutions to the Fractional-Stochastic Systems

Abstract

Fractional-stochastic differential equations are widely used tools to simulate a wide range of engineering and scientific phenomena. In this paper, the applicability of the approach of indeterminate coefficients to various fractional-stochastic models is examined. These models have a fractional white noise term and are mostly produced by fractional-order derivative operators. We also look into the application of a polynomial chaos algorithm to stochastic Lotka-Volterra and Benney systems. Fractional-stochastic equations are entirely novel systems that have the potential to function as models for a wide range of scientific and engineering phenomena. It is noted that fractional-order systems with uncertainty or a noise term can benefit from the effective use of Galerkin type approaches used in this article. Keywords: Galerkin method, Numerical solutions, Stochastic-fractional systems