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A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations

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Abstract

In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.

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Acknowledgments

The authors are very grateful to the reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper.

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Authors and Affiliations

  1. Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, Egypt

    Ramy M. Hafez & Samer S. Ezz-Eldien

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Ali H. Bhrawy

  3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Ali H. Bhrawy & Engy A. Ahmed

  4. Department of Mathematics, Cankaya University, Eskisehir Yolu 29 km, 06810, Ankara, Turkey

    Dumitru Baleanu

  5. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

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  1. Ramy M. Hafez
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  2. Samer S. Ezz-Eldien
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  3. Ali H. Bhrawy
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  4. Engy A. Ahmed
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  5. Dumitru Baleanu
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Correspondence to Dumitru Baleanu.

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Hafez, R.M., Ezz-Eldien, S.S., Bhrawy, A.H. et al. A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations. Nonlinear Dyn 82, 1431–1440 (2015). https://doi.org/10.1007/s11071-015-2250-7

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