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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Autores principales:	Sadullah Bulut, Mesut Karabacak, Hijaz Ahmad, Sameh Askar
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	<i>β</i>-conformable fractional derivative of Atangana (<i>G</i>′/<i>G</i>)-expansion method space–time fractional differential equations wave solution Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/666571dd87304f148e54946b4198560f
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spelling	oai:doaj.org-article:666571dd87304f148e54946b4198560f2021-11-25T19:06:04ZNew Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics10.3390/sym131120172073-8994https://doaj.org/article/666571dd87304f148e54946b4198560f2021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2017https://doaj.org/toc/2073-8994In 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.Sadullah BulutMesut KarabacakHijaz AhmadSameh AskarMDPI AGarticle<i>β</i>-conformable fractional derivative of Atangana(<i>G</i>′/<i>G</i>)-expansion methodspace–time fractional differential equationswave solutionMathematicsQA1-939ENSymmetry, Vol 13, Iss 2017, p 2017 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	<i>β</i>-conformable fractional derivative of Atangana (<i>G</i>′/<i>G</i>)-expansion method space–time fractional differential equations wave solution Mathematics QA1-939
spellingShingle	<i>β</i>-conformable fractional derivative of Atangana (<i>G</i>′/<i>G</i>)-expansion method space–time fractional differential equations wave solution Mathematics QA1-939 Sadullah Bulut Mesut Karabacak Hijaz Ahmad Sameh Askar New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics
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.
format	article
author	Sadullah Bulut Mesut Karabacak Hijaz Ahmad Sameh Askar
author_facet	Sadullah Bulut Mesut Karabacak Hijaz Ahmad Sameh Askar
author_sort	Sadullah Bulut
title	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_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_sort	new solitary and periodic wave solutions of (n + 1)-dimensional fractional order equations modeling fluid dynamics
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/666571dd87304f148e54946b4198560f
work_keys_str_mv	AT sadullahbulut newsolitaryandperiodicwavesolutionsofn1dimensionalfractionalorderequationsmodelingfluiddynamics AT mesutkarabacak newsolitaryandperiodicwavesolutionsofn1dimensionalfractionalorderequationsmodelingfluiddynamics AT hijazahmad newsolitaryandperiodicwavesolutionsofn1dimensionalfractionalorderequationsmodelingfluiddynamics AT samehaskar newsolitaryandperiodicwavesolutionsofn1dimensionalfractionalorderequationsmodelingfluiddynamics
_version_	1718410282110287872

New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics

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