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A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise

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  • Eftekhari, Tahereh
  • Rashidinia, Jalil

Abstract

In this research study, we present an efficient method based on the generalized hat functions for solving nonlinear stochastic differential equations driven by the multi-fractional Gaussian noise. Based on the generalized hat functions, we derive a stochastic operational matrix of the integral operator with respect to the variable order fractional Brownian motion, for the first time so far. Also, we establish a procedure to generate the variable order fractional Brownian motion. Then, we use them to provide numerical solutions for the proposed problems. In addition, the convergence of the new method is theoretically analyzed. Moreover, we solve the stochastic logistic equation, stochastic population growth model, and three test problems to confirm the efficiency of the new method. The obtained results are compared with other existing methods used for solving these problems.

Suggested Citation

  • Eftekhari, Tahereh & Rashidinia, Jalil, 2022. "A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322002922
    DOI: 10.1016/j.amc.2022.127218
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    References listed on IDEAS

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    1. Maleknejad, Khosrow & Rashidinia, Jalil & Eftekhari, Tahereh, 2018. "Numerical solution of three-dimensional Volterra–Fredholm integral equations of the first and second kinds based on Bernstein’s approximation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 272-285.
    2. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    3. Heydari, M.H. & Avazzadeh, Z. & Mahmoudi, M.R., 2019. "Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 105-124.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Zihan Zou & Yinfang Song & Chi Zhao, 2022. "Razumikhin Theorems on Polynomial Stability of Neutral Stochastic Pantograph Differential Equations with Markovian Switching," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    2. Tahereh Eftekhari & Jalil Rashidinia, 2023. "An Investigation on Existence, Uniqueness, and Approximate Solutions for Two-Dimensional Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 11(4), pages 1-29, February.

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