Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations
In this paper, the higher nonlinear problems of fractional advection-diffusion equations and systems of nonlinear fractional Burger’s equations are solved by using two sophisticated procedures, namely, the q-homotopy analysis transform method and the residual power series method. The proposed method...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/3666348 |
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| author | Hassan Khan Qasim Khan Fairouz Tchier null Ibrarullah Evren Hincal Gurpreet Singh F. M. O. Tawfiq Shahbaz Khan |
| author_facet | Hassan Khan Qasim Khan Fairouz Tchier null Ibrarullah Evren Hincal Gurpreet Singh F. M. O. Tawfiq Shahbaz Khan |
| author_sort | Hassan Khan |
| collection | DOAJ |
| description | In this paper, the higher nonlinear problems of fractional advection-diffusion equations and systems of nonlinear fractional Burger’s equations are solved by using two sophisticated procedures, namely, the q-homotopy analysis transform method and the residual power series method. The proposed methods are implemented with the Caputo operator. The present techniques are utilised in a very comprehensive and effective manner to obtain the solutions to the suggested fractional-order problems. The nonlinearity of the problem was controlled tactfully. The numerical results of a few examples are calculated and analyzed. The tables and graphs are constructed to understand the higher accuracy and applicability of the current method. The obtained results that are in good contact with the actual dynamics of the given problem, which is verified by the graphs and tables. The present techniques require fewer calculations and are associated with a higher degree of accuracy, and therefore can be extended to solve other high nonlinear fractional problems. |
| format | Article |
| id | doaj-art-8efee451eeab4141857105fd20577d06 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8efee451eeab4141857105fd20577d062025-02-03T01:22:42ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/3666348Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s EquationsHassan Khan0Qasim Khan1Fairouz Tchier2null Ibrarullah3Evren Hincal4Gurpreet Singh5F. M. O. Tawfiq6Shahbaz Khan7Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsSchool of Mathematical SciencesDepartment of MathematicsDepartment of MathematicsIn this paper, the higher nonlinear problems of fractional advection-diffusion equations and systems of nonlinear fractional Burger’s equations are solved by using two sophisticated procedures, namely, the q-homotopy analysis transform method and the residual power series method. The proposed methods are implemented with the Caputo operator. The present techniques are utilised in a very comprehensive and effective manner to obtain the solutions to the suggested fractional-order problems. The nonlinearity of the problem was controlled tactfully. The numerical results of a few examples are calculated and analyzed. The tables and graphs are constructed to understand the higher accuracy and applicability of the current method. The obtained results that are in good contact with the actual dynamics of the given problem, which is verified by the graphs and tables. The present techniques require fewer calculations and are associated with a higher degree of accuracy, and therefore can be extended to solve other high nonlinear fractional problems.http://dx.doi.org/10.1155/2022/3666348 |
| spellingShingle | Hassan Khan Qasim Khan Fairouz Tchier null Ibrarullah Evren Hincal Gurpreet Singh F. M. O. Tawfiq Shahbaz Khan Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations Journal of Function Spaces |
| title | Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations |
| title_full | Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations |
| title_fullStr | Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations |
| title_full_unstemmed | Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations |
| title_short | Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations |
| title_sort | numerical and analytical simulations of nonlinear time fractional advection and burger s equations |
| url | http://dx.doi.org/10.1155/2022/3666348 |
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