Comparative study of two techniques on some nonlinear problems based ussing conformable derivative
In this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate sol...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-12-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2020-0030 |
| _version_ | 1818362619393736704 |
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| author | Zulfiqar Aniqa Ahmad Jamshad |
| author_facet | Zulfiqar Aniqa Ahmad Jamshad |
| author_sort | Zulfiqar Aniqa |
| collection | DOAJ |
| description | In this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced differential transform method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are also presented and affirm that the considered methods are efficient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative. To explain the effects of several parameters and variables on the movement, the approximate results are shown in tables and two-and three-dimensional surface graphs. |
| first_indexed | 2024-12-13T21:35:28Z |
| format | Article |
| id | doaj.art-91d442d1a29e492db3d7b33dc4416163 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-13T21:35:28Z |
| publishDate | 2020-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-91d442d1a29e492db3d7b33dc44161632022-12-21T23:30:42ZengDe GruyterNonlinear Engineering2192-80102192-80292020-12-019147048210.1515/nleng-2020-0030nleng-2020-0030Comparative study of two techniques on some nonlinear problems based ussing conformable derivativeZulfiqar Aniqa0Ahmad Jamshad1Department of Mathematics, Faculty of Science, University of Gujrat, GujratPakistanDepartment of Mathematics, Faculty of Science, University of Gujrat, GujratPakistanIn this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced differential transform method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are also presented and affirm that the considered methods are efficient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative. To explain the effects of several parameters and variables on the movement, the approximate results are shown in tables and two-and three-dimensional surface graphs.https://doi.org/10.1515/nleng-2020-0030fractional calculusconformable fractional derivativereduced differential transform methodvariational iteration method |
| spellingShingle | Zulfiqar Aniqa Ahmad Jamshad Comparative study of two techniques on some nonlinear problems based ussing conformable derivative Nonlinear Engineering fractional calculus conformable fractional derivative reduced differential transform method variational iteration method |
| title | Comparative study of two techniques on some nonlinear problems based ussing conformable derivative |
| title_full | Comparative study of two techniques on some nonlinear problems based ussing conformable derivative |
| title_fullStr | Comparative study of two techniques on some nonlinear problems based ussing conformable derivative |
| title_full_unstemmed | Comparative study of two techniques on some nonlinear problems based ussing conformable derivative |
| title_short | Comparative study of two techniques on some nonlinear problems based ussing conformable derivative |
| title_sort | comparative study of two techniques on some nonlinear problems based ussing conformable derivative |
| topic | fractional calculus conformable fractional derivative reduced differential transform method variational iteration method |
| url | https://doi.org/10.1515/nleng-2020-0030 |
| work_keys_str_mv | AT zulfiqaraniqa comparativestudyoftwotechniquesonsomenonlinearproblemsbasedussingconformablederivative AT ahmadjamshad comparativestudyoftwotechniquesonsomenonlinearproblemsbasedussingconformablederivative |