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Afshin Babaei

Afshin Babaei

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-6980-9786
Education: PhD.
ScopusId: https://www.scopus.com/authid/detail.uri?authorId=57188696707
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
Phone: 011-35302418

Research

Title
A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay
Type
JournalPaper
Keywords
Stochastic delay equation (SFE), Fractional derivative, Step-by-step method, Legendre collocation scheme, Error analysis.
Year
2021
Journal Discrete and Continuous Dynamical Systems-Series S
DOI
Researchers ُSeddighe Banihashemi ، Hossein Jafari ، Afshin Babaei

Abstract

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.