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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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  • He, Lingyun
  • Banihashemi, Seddigheh
  • Jafari, Hossein
  • Babaei, Afshin

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.

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  • He, Lingyun & Banihashemi, Seddigheh & Jafari, Hossein & Babaei, Afshin, 2021. "Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:chsofr:v:149:y:2021:i:c:s0960077921003726
    DOI: 10.1016/j.chaos.2021.111018
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    References listed on IDEAS

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    1. Mirzaee, Farshid & Hadadiyan, Elham, 2017. "Solving system of linear Stratonovich Volterra integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 254-264.
    2. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    3. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 867-882.
    4. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    5. Das, S., 2009. "A note on fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2074-2079.
    6. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    7. Li, Qiang & Kang, Ting & Zhang, Qimin, 2018. "Mean-square dissipative methods for stochastic age-dependent capital system with fractional Brownian motion and jumps," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 81-92.
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    Cited by:

    1. Chendur Kumaran, R. & Venkatesh, T.G. & Swarup, K.S., 2022. "Stochastic delay differential equations: Analysis and simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Shu, Yadong & Li, Bo, 2022. "Existence and uniqueness of solutions to uncertain fractional switched systems with an uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Amr Abosenna & Ghada AlNemer & Boping Tian, 2024. "Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps," Mathematics, MDPI, vol. 12(13), pages 1-16, June.

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