Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients

The group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is extended to the certain subclasses of time fractional generalized KdV equations with initial and boundary values. Under the corresponding simil...

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Main Authors:	Cheng Chen, Yao-Lin Jiang, Xiao-Tian Wang
Format:	Article
Language:	English
Published:	MDPI AG 2019-10-01
Series:	Symmetry
Subjects:	infinitesimal operator riemann-liouville derivative initial and boundary value erdélyi-kober operator
Online Access:	https://www.mdpi.com/2073-8994/11/10/1281

id	doaj-f5b0bece742e4726bb2ddb2a15b74323
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spelling	doaj-f5b0bece742e4726bb2ddb2a15b743232020-11-25T02:16:16ZengMDPI AGSymmetry2073-89942019-10-011110128110.3390/sym11101281sym11101281Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable CoefficientsCheng Chen0Yao-Lin Jiang1Xiao-Tian Wang2School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710121, ChinaThe group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is extended to the certain subclasses of time fractional generalized KdV equations with initial and boundary values. Under the corresponding similarity transformation with similarity invariants, KdV equations with initial and boundary values have been transformed into fractional ordinary differential equations with initial value. Then we use the power series method to obtain the exact solution of the reduced equation with the Erdélyi-Kober fractional differential operator.https://www.mdpi.com/2073-8994/11/10/1281infinitesimal operatorriemann-liouville derivativeinitial and boundary valueerdélyi-kober operator
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Cheng Chen Yao-Lin Jiang Xiao-Tian Wang
spellingShingle	Cheng Chen Yao-Lin Jiang Xiao-Tian Wang Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients Symmetry infinitesimal operator riemann-liouville derivative initial and boundary value erdélyi-kober operator
author_facet	Cheng Chen Yao-Lin Jiang Xiao-Tian Wang
author_sort	Cheng Chen
title	Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients
title_short	Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients
title_full	Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients
title_fullStr	Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients
title_full_unstemmed	Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients
title_sort	lie symmetry analysis of the time fractional generalized kdv equations with variable coefficients
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2019-10-01
description	The group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is extended to the certain subclasses of time fractional generalized KdV equations with initial and boundary values. Under the corresponding similarity transformation with similarity invariants, KdV equations with initial and boundary values have been transformed into fractional ordinary differential equations with initial value. Then we use the power series method to obtain the exact solution of the reduced equation with the Erdélyi-Kober fractional differential operator.
topic	infinitesimal operator riemann-liouville derivative initial and boundary value erdélyi-kober operator
url	https://www.mdpi.com/2073-8994/11/10/1281
work_keys_str_mv	AT chengchen liesymmetryanalysisofthetimefractionalgeneralizedkdvequationswithvariablecoefficients AT yaolinjiang liesymmetryanalysisofthetimefractionalgeneralizedkdvequationswithvariablecoefficients AT xiaotianwang liesymmetryanalysisofthetimefractionalgeneralizedkdvequationswithvariablecoefficients
_version_	1724891566095466496

Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients

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