Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation
The main purpose of this paper is to apply the Lie symmetry analysis method for the two-dimensional time fractional Fokker-Planck (FP) equation in the sense of Riemann–Liouville fractional derivative. The Lie point symmetries are derived to obtain the similarity reductions and explicit solutions of...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/2490392 |
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| author | Nisrine Maarouf Khalid Hilal |
| author_facet | Nisrine Maarouf Khalid Hilal |
| author_sort | Nisrine Maarouf |
| collection | DOAJ |
| description | The main purpose of this paper is to apply the Lie symmetry analysis method for the two-dimensional time fractional Fokker-Planck (FP) equation in the sense of Riemann–Liouville fractional derivative. The Lie point symmetries are derived to obtain the similarity reductions and explicit solutions of the governing equation. By using the new conservation theorem, the new conserved vectors for the two-dimensional time fractional Fokker-Planck equation have been constructed with a detailed derivation. Finally, we obtain its explicit analytic solutions with the aid of the power series expansion method. |
| format | Article |
| id | doaj-art-85f74ee41ff74ecba88e9866b777c64a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-85f74ee41ff74ecba88e9866b777c64a2025-02-03T06:46:14ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/24903922490392Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck EquationNisrine Maarouf0Khalid Hilal1Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, P.O. Box 523, 23000 Beni Mellal, MoroccoLaboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, P.O. Box 523, 23000 Beni Mellal, MoroccoThe main purpose of this paper is to apply the Lie symmetry analysis method for the two-dimensional time fractional Fokker-Planck (FP) equation in the sense of Riemann–Liouville fractional derivative. The Lie point symmetries are derived to obtain the similarity reductions and explicit solutions of the governing equation. By using the new conservation theorem, the new conserved vectors for the two-dimensional time fractional Fokker-Planck equation have been constructed with a detailed derivation. Finally, we obtain its explicit analytic solutions with the aid of the power series expansion method.http://dx.doi.org/10.1155/2021/2490392 |
| spellingShingle | Nisrine Maarouf Khalid Hilal Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation Journal of Function Spaces |
| title | Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation |
| title_full | Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation |
| title_fullStr | Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation |
| title_full_unstemmed | Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation |
| title_short | Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation |
| title_sort | invariant analysis analytical solutions and conservation laws for two dimensional time fractional fokker planck equation |
| url | http://dx.doi.org/10.1155/2021/2490392 |
| work_keys_str_mv | AT nisrinemaarouf invariantanalysisanalyticalsolutionsandconservationlawsfortwodimensionaltimefractionalfokkerplanckequation AT khalidhilal invariantanalysisanalyticalsolutionsandconservationlawsfortwodimensionaltimefractionalfokkerplanckequation |