Toward computational algorithm for time-fractional Fokker–Planck models

This article describes an efficient algorithm based on residual power series to approximate the solution of a class of partial differential equations of time-fractional Fokker–Planck model. The fractional derivative is assumed in the Caputo sense. The proposed algorithm gives the solution in a form...

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Vydáno v:Advances in mechanical engineering Ročník 11; číslo 10
Hlavní autoři: Freihet, Asad, Hasan, Shatha, Alaroud, Mohammad, Al-Smadi, Mohammed, Ahmad, Rokiah Rozita, Salma Din, Ummul Khair
Médium: Journal Article
Jazyk:angličtina
Vydáno: London, England SAGE Publications 01.10.2019
Sage Publications Ltd
SAGE Publishing
Témata:
Algorithms
Fokker-Planck equation
Mathematical models
Partial differential equations
Perturbation
Power series
residual power series
numerical algorithms
Fokker–Planck equation
Caputo fractional derivatives
ISSN:1687-8132, 1687-8140
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Shrnutí:This article describes an efficient algorithm based on residual power series to approximate the solution of a class of partial differential equations of time-fractional Fokker–Planck model. The fractional derivative is assumed in the Caputo sense. The proposed algorithm gives the solution in a form of rapidly convergent fractional power series with easily computable coefficients. It does not require linearization, discretization, or small perturbation. To test simplicity, potentiality, and practical usefulness of the proposed algorithm, illustrative examples are provided. The approximate solutions of time-fractional Fokker–Planck equations are obtained by the residual power series method are compared with those obtained by other existing methods. The present results and graphics reveal the ability of residual power series method to deal with a wide range of partial fractional differential equations emerging in the modeling of physical phenomena of science and engineering.
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ISSN:1687-8132
1687-8140
DOI:10.1177/1687814019881039