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Strong convergence of a Euler–Maruyama method for fractional stochastic Langevin equations

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  • Ahmadova, Arzu
  • Mahmudov, Nazim I.

Abstract

The novelty of this paper is to derive a mild solution by means of recently defined Mittag-Leffler type functions of fractional stochastic Langevin equations of orders α∈(1,2] and β∈(0,1] whose coefficients satisfy standard Lipschitz and linear growth conditions. Then, we prove existence and uniqueness results of mild solution and show the coincidence between the notion of mild solution and integral equation. For this class of system, we construct fractional Euler–Maruyama method and establish new results on strong convergence of this method for fractional stochastic Langevin equations. We also introduce a general form of the nonlinear fractional stochastic Langevin equation and derive a general mild solution. Finally, the numerical examples are illustrated to verify the main theory.

Suggested Citation

  • Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Strong convergence of a Euler–Maruyama method for fractional stochastic Langevin equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 429-448.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:429-448
    DOI: 10.1016/j.matcom.2021.05.037
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    References listed on IDEAS

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    1. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Pedjeu, Jean-C. & Ladde, Gangaram S., 2012. "Stochastic fractional differential equations: Modeling, method and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 279-293.
    3. Zhang, Tong & Li, ShiShun, 2017. "A posteriori error estimates of finite element method for the time-dependent Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 13-26.
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