Fractional-Order Genocchi–Petrov–Galerkin Method for Solving Time–Space Fractional Fokker–Planck Equations Arising from the Physical Phenomenon

Abstract

In the current study, we present the fractional-order Genocchi–Petrov–Galerkin method to investigate the approximate solution of time–space fractional Fokker–Planck equations (FFPEs). In the proposed approach, due to fractional Genocchi functions (FGFs) and their operational matrices transform these equations into a system of algebraic equations. The operational matrices of fractional-order integration and derivative are obtained by utilizing Riemann–Liouville fractional integral operator and Caputo fractional derivative, respectively. The convergence analysis of the proposed technique is rigorously discussed. To illustrate the applicability of the error formulas, we present the process of obtaining results for some examples. These examples are carried out to confirm the effectiveness of the proposed method.

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Acknowledgements

We express our sincere thanks to the anonymous referees for valuable suggestions that improved the final manuscript.

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Correspondence to Yadollah Ordokhani.

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Dehestani, H., Ordokhani, Y. & Razzaghi, M. Fractional-Order Genocchi–Petrov–Galerkin Method for Solving Time–Space Fractional Fokker–Planck Equations Arising from the Physical Phenomenon. Int. J. Appl. Comput. Math 6, 100 (2020). https://doi.org/10.1007/s40819-020-00859-6

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Keywords

  • Fractional-order Genocchi functions
  • Fractional Fokker–Planck equations
  • Petrov–Galerkin method
  • Operational matrix
  • Error analysis

Mathematics Subject Classification

  • 26A33
  • 65N30
  • 65M15