Efficient Solutions for Stochastic Fractional Differential Equations with a Neutral Delay Using Jacobi Poly-Fractonomials

Afshin Babaei, Sedigheh Banihashemi, Behrouz Parsa Moghaddam, Arman Dabiri and Alexandra Galhano ()
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Afshin Babaei: Department of Applied Mathematics, University of Mazandaran, Babolsar P.O. Box 47416-95447, Iran
Sedigheh Banihashemi: Department of Applied Mathematics, University of Mazandaran, Babolsar P.O. Box 47416-95447, Iran
Behrouz Parsa Moghaddam: Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran
Arman Dabiri: Department of Mechanical and Mechatronics, Southern Illinois University, Edwardsville, IL 62026, USA
Alexandra Galhano: Faculdade de Ciências Naturais, Engenharias e Tecnologias, Universidade Lusófona do Porto, Rua Augusto Rosa 24, 4000-098 Porto, Portugal

Mathematics, 2024, vol. 12, issue 20, 1-20

Abstract: 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.

Keywords: fractional neutral stochastic differential equations; Caputo fractional derivative; time-varying delay; iterative collocation method; Jacobi poly-fractonomials; numerical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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