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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
Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme
Type
JournalPaper
Keywords
Fractional calculus,Stochastic delay system, Step-by-step method, Legendre collocation scheme, Convergence analysis
Year
2021
Journal CHAOS SOLITONS & FRACTALS
DOI
Researchers Lingyun He ، ُSeddighe Banihashemi ، Hossein Jafari ، Afshin Babaei

Abstract

In this article, a step-by-step collocation approach based on the shifted Legendre polynomials is presented to solve a fractional order system of nonlinear stochastic differential equations involving a constant delay. The problem is considered with suitable initial condition and the fractional derivative is in the Caputo sense. With a step-by-step process, first, the considered problem is converted into a non-delay fractional order system of nonlinear stochastic differential equations in each step and then, a shifted Legendre collocation scheme is introduced to solve this system. By collocating the obtained residual at the shifted Legendre points, we get a nonlinear system of equations in each step. The convergence analysis and rate of convergence of the proposed method are investigated . Finally, three test examples are provided to affirm the accuracy of this technique in the presence of different noise measures.