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Numerical solution for fractional model of Fokker-Planck equation by using q-HATM

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  • Prakash, Amit
  • Kaur, Hardish

Abstract

In this paper, we present a hybrid computational algorithm which is an inventive reconciliation of q-homotopy analysis method (q-HAM) and Laplace transform (LT) to procure the solution of time- fractional and space-time fractional Fokker-Planck equation. The proposed method gives an analytical solution in the form of a convergent series with easily computable components. The outcomes disclose that the present approach is user friendly and an appropriate selection of auxiliary parameters h and n (n ≥ 1) gives more correct approximations identical to exact solution. The auxiliary parameter h in q-HATM provides a convenient way of controlling the convergence region of series solutions.

Suggested Citation

  • Prakash, Amit & Kaur, Hardish, 2017. "Numerical solution for fractional model of Fokker-Planck equation by using q-HATM," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 99-110.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:99-110
    DOI: 10.1016/j.chaos.2017.10.003
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    References listed on IDEAS

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    1. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    2. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
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    Cited by:

    1. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    2. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    3. Prakash, Amit & Kaur, Hardish, 2019. "Analysis and numerical simulation of fractional order Cahn–Allen model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 134-142.

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