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Title
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Efficient Solutions for Stochastic Fractional Differential Equations with a Neutral Delay Using Jacobi Poly-Fractonomials
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Type
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JournalPaper
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Keywords
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fractional neutral stochastic differential equations, Caputo fractional derivative, time-varying delay, iterative collocation method, Jacobi poly-fractonomials, numerical solution
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Abstract
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This paper introduces a novel numerical technique for solving fractional stochastic differential equations with neutral delays. The method employs a stepwise collocation scheme with Jacobi poly-fractonomials to consider unknown stochastic processes. For this purpose, the delay differential equations are transformed into augmented ones without delays. This transformation makes it possible to use a collocation scheme improved with Jacobi poly-fractonomials to solve the changed equations repeatedly. At each iteration, a system of nonlinear equations is generated. Next, the convergence properties of the proposed method are rigorously analyzed. Afterward, the practical utility of the proposed numerical technique is validated through a series of test examples. These examples illustrate the method’s capability to produce accurate and efficient solutions.
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Researchers
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Alexandra Galhano (Fifth Researcher), Arman Dabiri (Fourth Researcher), Behrouz Parsa Moghaddam (Third Researcher), ُSeddighe Banihashemi (Second Researcher), Afshin Babaei (First Researcher)
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