Exploring the Exact Solution of the Space-Fractional Stochastic Regularized Long Wave Equation: A Bifurcation Approach

被引：0

作者：

Almutairi, Bashayr ^{[1
]}

Al Nuwairan, Muneerah ^{[1
]}

Aldhafeeri, Anwar ^{[1
]}

机构：

[1] King Faisal Univ, Coll Sci, Dept Math & Stat, POB 400, Al Hasa 31982, Saudi Arabia

来源：

FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 05期

关键词：

stochastic fractional differential equations; long wave equation; bifurcation method; modified Rieman-Liouville derivative; DIFFERENTIAL-EQUATIONS; MODEL;

D O I：

10.3390/fractalfract8050298

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This study explores the effects of using space-fractional derivatives and adding multiplicative noise, modeled by a Wiener process, on the solutions of the space-fractional stochastic regularized long wave equation. New fractional stochastic solutions are constructed, and the consistency of the obtained solutions is examined using the transition between phase plane orbits. Their bifurcation and dependence on initial conditions are investigated. Some of these solutions are shown graphically, illustrating both the individual and combined influences of fractional order and noise on selected solutions. These effects appear as alterations in the amplitude and width of the solutions, and as variations in their smoothness.

引用

页数：14

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