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Title
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Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme
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Type
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JournalPaper
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Keywords
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Fractional calculus,Stochastic delay system, Step-by-step method, Legendre collocation scheme, Convergence analysis
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Abstract
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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.
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Researchers
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Hossein Jafari (Third Researcher), Afshin Babaei (Fourth Researcher), ُSeddighe Banihashemi (Second Researcher), Lingyun He (First Researcher)
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