Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients
The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. The classical Burgers equation is generalized by considering the generalized Atangana-Baleanu time-fractional derivative. The studied model contains as particular...
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| Main Authors: | , , , |
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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/10.1155/2021/8803182 |
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| _version_ | 1832558038468263936 |
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| author | Dumitru Vieru Constantin Fetecau Nehad Ali Shah Jae Dong Chung |
| author_facet | Dumitru Vieru Constantin Fetecau Nehad Ali Shah Jae Dong Chung |
| author_sort | Dumitru Vieru |
| collection | DOAJ |
| description | The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. The classical Burgers equation is generalized by considering the generalized Atangana-Baleanu time-fractional derivative. The studied model contains as particular cases the Burgers equation with Atangana-Baleanu, Caputo-Fabrizio, and Caputo time-fractional derivatives. A numerical scheme, based on the finite-difference approximations and some integral representations of the two-parameter Mittag-Leffler functions, has been developed. Numerical solutions of a particular problem with initial and boundary values are determined by employing the proposed method. The numerical results are plotted to compare solutions corresponding to the problems with time-fractional derivatives with different kernels. |
| format | Article |
| id | doaj-art-705a7c2629814ca6acd27536961d72cf |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-705a7c2629814ca6acd27536961d72cf2025-02-03T01:33:21ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/8803182Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable CoefficientsDumitru Vieru0Constantin Fetecau1Nehad Ali Shah2Jae Dong Chung3Department of Theoretical MechanicsSection of MathematicsDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringThe generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. The classical Burgers equation is generalized by considering the generalized Atangana-Baleanu time-fractional derivative. The studied model contains as particular cases the Burgers equation with Atangana-Baleanu, Caputo-Fabrizio, and Caputo time-fractional derivatives. A numerical scheme, based on the finite-difference approximations and some integral representations of the two-parameter Mittag-Leffler functions, has been developed. Numerical solutions of a particular problem with initial and boundary values are determined by employing the proposed method. The numerical results are plotted to compare solutions corresponding to the problems with time-fractional derivatives with different kernels.http://dx.doi.org/10.1155/2021/8803182 |
| spellingShingle | Dumitru Vieru Constantin Fetecau Nehad Ali Shah Jae Dong Chung Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients Journal of Function Spaces |
| title | Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients |
| title_full | Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients |
| title_fullStr | Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients |
| title_full_unstemmed | Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients |
| title_short | Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients |
| title_sort | numerical approaches of the generalized time fractional burgers equation with time variable coefficients |
| url | http://dx.doi.org/10.1155/2021/8803182 |
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