New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics
In this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semant...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2017 |
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| author | Sadullah Bulut Mesut Karabacak Hijaz Ahmad Sameh Askar |
| author_facet | Sadullah Bulut Mesut Karabacak Hijaz Ahmad Sameh Askar |
| author_sort | Sadullah Bulut |
| collection | DOAJ |
| description | In this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mfrac><msup><mi>G</mi><mo>′</mo></msup><mi>G</mi></mfrac><mo>)</mo></mrow></semantics></math></inline-formula>-expansion method under Atangana’s definition of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-conformable fractional derivative to obtain the exact solutions of the space–time fractional differential equations, which have attracted the attention of many researchers recently. The method is applied to different versions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional Kadomtsev–Petviashvili equations and new exact solutions of these equations depending on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> parameter are acquired. If the parameter values in the new solutions obtained are selected appropriately, 2D and 3D graphs are plotted. Thus, the decay and symmetry properties of solitary wave solutions in a nonlocal shallow water wave model are investigated. It is also shown that all such solitary wave solutions are symmetrical on both sides of the apex. In addition, a close relationship is established between symmetric and propagated wave solutions. |
| first_indexed | 2024-03-10T05:01:10Z |
| format | Article |
| id | doaj.art-666571dd87304f148e54946b4198560f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:01:10Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-666571dd87304f148e54946b4198560f2023-11-23T01:43:28ZengMDPI AGSymmetry2073-89942021-10-011311201710.3390/sym13112017New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid DynamicsSadullah Bulut0Mesut Karabacak1Hijaz Ahmad2Sameh Askar3Department of Mathematics, Erzurum Technical University, Erzurum 25050, TurkeyDepartment of Mathematics, Atatürk University, Erzurum 25400, TurkeySection of Mathematics, International Telematic University Uninettuno, 00186 Roma, ItalyDepartment of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaIn this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mfrac><msup><mi>G</mi><mo>′</mo></msup><mi>G</mi></mfrac><mo>)</mo></mrow></semantics></math></inline-formula>-expansion method under Atangana’s definition of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-conformable fractional derivative to obtain the exact solutions of the space–time fractional differential equations, which have attracted the attention of many researchers recently. The method is applied to different versions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional Kadomtsev–Petviashvili equations and new exact solutions of these equations depending on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> parameter are acquired. If the parameter values in the new solutions obtained are selected appropriately, 2D and 3D graphs are plotted. Thus, the decay and symmetry properties of solitary wave solutions in a nonlocal shallow water wave model are investigated. It is also shown that all such solitary wave solutions are symmetrical on both sides of the apex. In addition, a close relationship is established between symmetric and propagated wave solutions.https://www.mdpi.com/2073-8994/13/11/2017<i>β</i>-conformable fractional derivative of Atangana(<i>G</i>′/<i>G</i>)-expansion methodspace–time fractional differential equationswave solution |
| spellingShingle | Sadullah Bulut Mesut Karabacak Hijaz Ahmad Sameh Askar New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics Symmetry <i>β</i>-conformable fractional derivative of Atangana (<i>G</i>′/<i>G</i>)-expansion method space–time fractional differential equations wave solution |
| title | New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics |
| title_full | New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics |
| title_fullStr | New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics |
| title_full_unstemmed | New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics |
| title_short | New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics |
| title_sort | new solitary and periodic wave solutions of n 1 dimensional fractional order equations modeling fluid dynamics |
| topic | <i>β</i>-conformable fractional derivative of Atangana (<i>G</i>′/<i>G</i>)-expansion method space–time fractional differential equations wave solution |
| url | https://www.mdpi.com/2073-8994/13/11/2017 |
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