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Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation

Author

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  • Rui, Weiguo
  • Yang, Xinsong
  • Chen, Fen

Abstract

In this paper, the traditional separation method of variables is improved by fixing a part of the variables called the separation method of semi-fixed variables. By using this improved method, the time-fractional Fokker–Planck equation with external force field is studied. Some new exact solutions and dynamical properties of the equation are investigated in various external potential functions such as linear potential, harmonic potential, logarithmic potential, exponential potential, and quartic potential. Some interesting dynamical behaviors and phenomena are discovered. The profiles of several representative exact solutions are illustrated by 3D-graphs and 2D-graphs

Suggested Citation

  • Rui, Weiguo & Yang, Xinsong & Chen, Fen, 2022. "Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    • Handle: RePEc:eee:phsmap:v:595:y:2022:i:c:s0378437122001194
    DOI: 10.1016/j.physa.2022.127068
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    References listed on IDEAS

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    1. Lenzi, E.K. & Malacarne, L.C. & Mendes, R.S. & Pedron, I.T., 2003. "Anomalous diffusion, nonlinear fractional Fokker–Planck equation and solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 245-252.
    2. So, F. & Liu, K.L., 2004. "A study of the subdiffusive fractional Fokker–Planck equation of bistable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 378-390.
    3. Caldas, Denise & Chahine, Jorge & Filho, Elso Drigo, 2014. "The Fokker–Planck equation for a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 92-100.
    4. Rui, Weiguo, 2018. "Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 158-171.
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