Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method

Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method

In this paper, the time-fractional Fujimoto–Watanabe equation is investigated using the Riemann–Liouville fractional derivative. Symmetry groups and similarity reductions are obtained by virtue of the Lie symmetry analysis approach. Meanwhile, the time-fractional Fujimoto–Watanabe equation is transf...

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Main Authors: Baoyong Guo, Huanhe Dong, Yong Fang
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/4830684
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spelling doaj-c2d3cd2627b24bc7834d3fe73302887a2020-11-25T02:04:12ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/48306844830684Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis MethodBaoyong Guo0Huanhe Dong1Yong Fang2College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this paper, the time-fractional Fujimoto–Watanabe equation is investigated using the Riemann–Liouville fractional derivative. Symmetry groups and similarity reductions are obtained by virtue of the Lie symmetry analysis approach. Meanwhile, the time-fractional Fujimoto–Watanabe equation is transformed into three kinds of reduced equations and the third of which is based on Erdélyi–Kober fractional integro-differential operators. Furthermore, the conservation laws are also acquired by Ibragimov’s theory.http://dx.doi.org/10.1155/2020/4830684
collection DOAJ
language English
format Article
sources DOAJ
author Baoyong Guo
Huanhe Dong
Yong Fang
spellingShingle Baoyong Guo
Huanhe Dong
Yong Fang
Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method
Complexity
author_facet Baoyong Guo
Huanhe Dong
Yong Fang
author_sort Baoyong Guo
title Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method
title_short Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method
title_full Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method
title_fullStr Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method
title_full_unstemmed Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method
title_sort symmetry groups, similarity reductions, and conservation laws of the time-fractional fujimoto–watanabe equation using lie symmetry analysis method
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
description In this paper, the time-fractional Fujimoto–Watanabe equation is investigated using the Riemann–Liouville fractional derivative. Symmetry groups and similarity reductions are obtained by virtue of the Lie symmetry analysis approach. Meanwhile, the time-fractional Fujimoto–Watanabe equation is transformed into three kinds of reduced equations and the third of which is based on Erdélyi–Kober fractional integro-differential operators. Furthermore, the conservation laws are also acquired by Ibragimov’s theory.
url http://dx.doi.org/10.1155/2020/4830684
work_keys_str_mv AT baoyongguo symmetrygroupssimilarityreductionsandconservationlawsofthetimefractionalfujimotowatanabeequationusingliesymmetryanalysismethod
AT huanhedong symmetrygroupssimilarityreductionsandconservationlawsofthetimefractionalfujimotowatanabeequationusingliesymmetryanalysismethod
AT yongfang symmetrygroupssimilarityreductionsandconservationlawsofthetimefractionalfujimotowatanabeequationusingliesymmetryanalysismethod
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