On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science
The purpose of this article is to construct some novel exact travelling and solitary wave solutions of the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky equation, and two different forms of integration schemes have been utilized in this context. As a result, a variety of bright and dar...
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De Gruyter
2020-11-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2020-0188 |
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doaj-e522d5cafcd348e4aaa8a8ea0ccd96752021-09-05T13:59:38ZengDe GruyterOpen Physics2391-54712020-11-0118180681910.1515/phys-2020-0188phys-2020-0188On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical scienceAkhtar Junaid0Seadawy Aly R.1Tariq Kalim U.2Baleanu Dumitru3Department of Mathematics, Mirpur University of Science and Technology, Mirpur, 10250 (AJK), PakistanMathematics Department, Faculty of science, Taibah University, Al-Madinah Al-Munawarah, Saudi ArabiaDepartment of Mathematics, Mirpur University of Science and Technology, Mirpur, 10250 (AJK), PakistanDepartment of Mathematics, Cankaya University, Ankara, TurkeyThe purpose of this article is to construct some novel exact travelling and solitary wave solutions of the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky equation, and two different forms of integration schemes have been utilized in this context. As a result, a variety of bright and dark solitons, kink- and antikink-type solitons, hyperbolic functions, trigonometric functions, elliptic functions, periodic solitary wave solutions and travelling wave solutions are obtained, and the sufficient conditions for the existence of solution are also discussed. Moreover, some of the obtained solutions are illustrated as two- and three-dimensional graphical images by using computational software Mathematica. These types of solutions have a wide range of applications in applied sciences and mathematical physics. The proposed methods are very useful for solving nonlinear partial differential equations arising in physical science and engineering.https://doi.org/10.1515/phys-2020-0188fractional konopelchenko–dubrovsky equationjumarie’s modified riemann–liouvilleunified riccati equation expansionmodified extended auxiliary equation mapping method |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Akhtar Junaid Seadawy Aly R. Tariq Kalim U. Baleanu Dumitru |
| spellingShingle |
Akhtar Junaid Seadawy Aly R. Tariq Kalim U. Baleanu Dumitru On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science Open Physics fractional konopelchenko–dubrovsky equation jumarie’s modified riemann–liouville unified riccati equation expansion modified extended auxiliary equation mapping method |
| author_facet |
Akhtar Junaid Seadawy Aly R. Tariq Kalim U. Baleanu Dumitru |
| author_sort |
Akhtar Junaid |
| title |
On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science |
| title_short |
On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science |
| title_full |
On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science |
| title_fullStr |
On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science |
| title_full_unstemmed |
On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science |
| title_sort |
on some novel exact solutions to the time fractional (2 + 1) dimensional konopelchenko–dubrovsky system arising in physical science |
| publisher |
De Gruyter |
| series |
Open Physics |
| issn |
2391-5471 |
| publishDate |
2020-11-01 |
| description |
The purpose of this article is to construct some novel exact travelling and solitary wave solutions of the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky equation, and two different forms of integration schemes have been utilized in this context. As a result, a variety of bright and dark solitons, kink- and antikink-type solitons, hyperbolic functions, trigonometric functions, elliptic functions, periodic solitary wave solutions and travelling wave solutions are obtained, and the sufficient conditions for the existence of solution are also discussed. Moreover, some of the obtained solutions are illustrated as two- and three-dimensional graphical images by using computational software Mathematica. These types of solutions have a wide range of applications in applied sciences and mathematical physics. The proposed methods are very useful for solving nonlinear partial differential equations arising in physical science and engineering. |
| topic |
fractional konopelchenko–dubrovsky equation jumarie’s modified riemann–liouville unified riccati equation expansion modified extended auxiliary equation mapping method |
| url |
https://doi.org/10.1515/phys-2020-0188 |
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