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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Afshin Babaei & Sedigheh Banihashemi & Behrouz Parsa Moghaddam & Arman Dabiri & Alexandra Galhano, 2024. "Efficient Solutions for Stochastic Fractional Differential Equations with a Neutral Delay Using Jacobi Poly-Fractonomials," Mathematics, MDPI, vol. 12(20), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3273-:d:1501861
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    References listed on IDEAS

    as
    1. Ayazi, N. & Mokhtary, P. & Moghaddam, B. Parsa, 2024. "Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. B. Parsa Moghaddam & A. Dabiri & Z. S. Mostaghim & Z. Moniri, 2023. "Numerical solution of fractional dynamical systems with impulsive effects," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-15, January.
    3. Xin Chen & Peng Hu & Stephen Shum & Yuhan Zhang, 2016. "Dynamic Stochastic Inventory Management with Reference Price Effects," Operations Research, INFORMS, vol. 64(6), pages 1529-1536, December.
    4. Rahimkhani, P. & Ordokhani, Y., 2022. "Chelyshkov least squares support vector regression for nonlinear stochastic differential equations by variable fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    Full references (including those not matched with items on IDEAS)

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