Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative

Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative

The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional der...

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Main Authors: Majid Bagheri, Ali Khani
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/8819183
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spelling doaj-6de8f84df0af4e1f80e4f5ab63e2285b2021-07-02T17:28:37ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/88191838819183Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional DerivativeMajid Bagheri0Ali Khani1Faculty of Science, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranFaculty of Science, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranThe present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena.http://dx.doi.org/10.1155/2020/8819183
collection DOAJ
language English
format Article
sources DOAJ
author Majid Bagheri
Ali Khani
spellingShingle Majid Bagheri
Ali Khani
Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
Advances in Mathematical Physics
author_facet Majid Bagheri
Ali Khani
author_sort Majid Bagheri
title Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
title_short Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
title_full Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
title_fullStr Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
title_full_unstemmed Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
title_sort analytical method for solving the fractional order generalized kdv equation by a beta-fractional derivative
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2020-01-01
description The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena.
url http://dx.doi.org/10.1155/2020/8819183
work_keys_str_mv AT majidbagheri analyticalmethodforsolvingthefractionalordergeneralizedkdvequationbyabetafractionalderivative
AT alikhani analyticalmethodforsolvingthefractionalordergeneralizedkdvequationbyabetafractionalderivative
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