A NOVEL COLLOCATION APPROACH TO SOLVE A FRACTIONAL ORDER INVOLVING A CONSTANT DELAY

被引：12

作者：

Banihashemi, Seddigheh ^{[1
]}

Jafaria, Hossein ^{[1
,2
,3
,4
]}

Babaei, Afshin ^{[1
]}

机构：

[1] Univ Mazandaran, Dept Math, Babolsar, Iran

[2] Univ South Africa, Dept Math Sci, UNISA, ZA-0003 Pretoria, South Africa

[3] China Med Univ, Dept Med Res, China Med Univ Hosp, Taichung 110122, Taiwan

[4] Azerbaijan Univ, Dept Math & Informat, Jeyhun Hajibeyli 71, AZ-1007 Baku, Azerbaijan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2022年 / 15卷 / 02期

关键词：

  Stochastic delay equation (SFE); Fractional derivative; Step-by-step method; Legendre collocation scheme; Error analysis; STOCHASTIC DIFFERENTIAL-EQUATIONS; MODEL; APPROXIMATION; SYSTEM;

D O I：

10.3934/dcdss.2021025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In present work, a step-by-step Legendre collocation method is employed to solve a class of nonlinear fractional stochastic delay differential equations (FSDDEs). The step-by-step method converts the nonlinear FSDDE into a non-delay nonlinear fractional stochastic differential equation (FSDE). Then, a Legendre collocation approach is considered to obtain the numerical solution in each step. By using a collocation scheme, the non-delay nonlinear FSDE is reduced to a nonlinear system. Moreover, the error analysis of this numerical approach is investigated and convergence rate is examined. The accuracy and reliability of this method is shown on three test examples and the effect of different noise measures is investigated. Finally, as an useful application, the proposed scheme is applied to obtain the numerical solution of a stochastic SIRS model.

引用

页码：339 / 357

页数：19

共 45 条

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