Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation

Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation

The potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work, the modified auxiliary equation technique an...

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Main Authors: Ghazala Akram, Maasoomah Sadaf, Maria Sarfraz, Nageela Anum
Format: Article
Language:English
Published: Elsevier 2022-01-01
Series:Alexandria Engineering Journal
Subjects:
Wave solutions
Modified auxiliary equation method
Residual power series method
Caputo fractional derivative
Jumarie’s modified Riemann-Liouville derivative
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016821003811
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spelling doaj-b3c4ecd0ed4e4efdbbba65873312ea122021-07-31T04:37:40ZengElsevierAlexandria Engineering Journal1110-01682022-01-01611501509Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equationGhazala Akram0Maasoomah Sadaf1Maria Sarfraz2Nageela Anum3Corresponding author.; Department of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanThe potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work, the modified auxiliary equation technique and residual power series method are utilized to build new exact and analytical approximate solutions of the time-fractional potential Korteweg-de Vries equation. The dynamics of the solutions obtained are explored by drawing them in two and three dimensions. Comparisons between the new results and the solutions available in literature show that the presented approaches of nonlinear problem resolution are highly effective and reliable. The obtained solutions will be helpful to understand the dynamical framework of many nonlinear physical phenomena.http://www.sciencedirect.com/science/article/pii/S1110016821003811Wave solutionsModified auxiliary equation methodResidual power series methodCaputo fractional derivativeJumarie’s modified Riemann-Liouville derivative
collection DOAJ
language English
format Article
sources DOAJ
author Ghazala Akram
Maasoomah Sadaf
Maria Sarfraz
Nageela Anum
spellingShingle Ghazala Akram
Maasoomah Sadaf
Maria Sarfraz
Nageela Anum
Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
Alexandria Engineering Journal
Wave solutions
Modified auxiliary equation method
Residual power series method
Caputo fractional derivative
Jumarie’s modified Riemann-Liouville derivative
author_facet Ghazala Akram
Maasoomah Sadaf
Maria Sarfraz
Nageela Anum
author_sort Ghazala Akram
title Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
title_short Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
title_full Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
title_fullStr Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
title_full_unstemmed Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
title_sort dynamics investigation of (1+1)-dimensional time-fractional potential korteweg-de vries equation
publisher Elsevier
series Alexandria Engineering Journal
issn 1110-0168
publishDate 2022-01-01
description The potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work, the modified auxiliary equation technique and residual power series method are utilized to build new exact and analytical approximate solutions of the time-fractional potential Korteweg-de Vries equation. The dynamics of the solutions obtained are explored by drawing them in two and three dimensions. Comparisons between the new results and the solutions available in literature show that the presented approaches of nonlinear problem resolution are highly effective and reliable. The obtained solutions will be helpful to understand the dynamical framework of many nonlinear physical phenomena.
topic Wave solutions
Modified auxiliary equation method
Residual power series method
Caputo fractional derivative
Jumarie’s modified Riemann-Liouville derivative
url http://www.sciencedirect.com/science/article/pii/S1110016821003811
work_keys_str_mv AT ghazalaakram dynamicsinvestigationof11dimensionaltimefractionalpotentialkortewegdevriesequation
AT maasoomahsadaf dynamicsinvestigationof11dimensionaltimefractionalpotentialkortewegdevriesequation
AT mariasarfraz dynamicsinvestigationof11dimensionaltimefractionalpotentialkortewegdevriesequation
AT nageelaanum dynamicsinvestigationof11dimensionaltimefractionalpotentialkortewegdevriesequation
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