Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative
In this paper, group analysis of the time fractional Harry-Dym equation with Riemann–Liouville derivative is performed. Its maximal symmetry group in Lie’s sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equation under study are performed. As a re...
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| Veröffentlicht in: | Physica A 2014-09, Vol.409, p.110-118 |
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| creator | Huang, Qing Zhdanov, Renat |
| description | In this paper, group analysis of the time fractional Harry-Dym equation with Riemann–Liouville derivative is performed. Its maximal symmetry group in Lie’s sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equation under study are performed. As a result, the reduced fractional ordinary differential equations are deduced, and some group invariant solutions in explicit form are obtained as well.
•Lie classical method is used to investigate the time fractional Harry-Dym equation.•The maximal Lie symmetry group of the equation under study is derived.•Optimal system of subgroups are determined and the optimization of the system is proved.•Reduced fractional ODEs and some exact solutions in explicit forms are presented.•The approach used here can also be applied to other nonlinear fractional PDEs. |
| doi_str_mv | 10.1016/j.physa.2014.04.043 |
| format | Article |
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•Lie classical method is used to investigate the time fractional Harry-Dym equation.•The maximal Lie symmetry group of the equation under study is derived.•Optimal system of subgroups are determined and the optimization of the system is proved.•Reduced fractional ODEs and some exact solutions in explicit forms are presented.•The approach used here can also be applied to other nonlinear fractional PDEs.</description><identifier>ISSN: 0378-4371</identifier><identifier>EISSN: 1873-2119</identifier><identifier>DOI: 10.1016/j.physa.2014.04.043</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Derivatives ; Differential equations ; Exact solutions ; Fractional Harry-Dym equation ; Group-invariant solution ; Invariants ; Lie symmetry ; Mathematical analysis ; Optimal system ; Optimization ; Riemann–Liouville derivative ; Similarity ; Symmetry</subject><ispartof>Physica A, 2014-09, Vol.409, p.110-118</ispartof><rights>2014 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-15d771d53c419290100db51058907632d9b016a42a00c3d1f820bf01a395513</citedby><cites>FETCH-LOGICAL-c336t-15d771d53c419290100db51058907632d9b016a42a00c3d1f820bf01a395513</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.physa.2014.04.043$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Huang, Qing</creatorcontrib><creatorcontrib>Zhdanov, Renat</creatorcontrib><title>Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative</title><title>Physica A</title><description>In this paper, group analysis of the time fractional Harry-Dym equation with Riemann–Liouville derivative is performed. Its maximal symmetry group in Lie’s sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equation under study are performed. As a result, the reduced fractional ordinary differential equations are deduced, and some group invariant solutions in explicit form are obtained as well.
•Lie classical method is used to investigate the time fractional Harry-Dym equation.•The maximal Lie symmetry group of the equation under study is derived.•Optimal system of subgroups are determined and the optimization of the system is proved.•Reduced fractional ODEs and some exact solutions in explicit forms are presented.•The approach used here can also be applied to other nonlinear fractional PDEs.</description><subject>Derivatives</subject><subject>Differential equations</subject><subject>Exact solutions</subject><subject>Fractional Harry-Dym equation</subject><subject>Group-invariant solution</subject><subject>Invariants</subject><subject>Lie symmetry</subject><subject>Mathematical analysis</subject><subject>Optimal system</subject><subject>Optimization</subject><subject>Riemann–Liouville derivative</subject><subject>Similarity</subject><subject>Symmetry</subject><issn>0378-4371</issn><issn>1873-2119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEuXxBWy8ZJMyEzdNvGCBeEuVkIC95doT1VUexXYK2fEP_CFfQkJZI4000p1zR7qXsTOEKQLOL9bTzaoPepoCzqYwjthjEyxykaSIcp9NQORFMhM5HrKjENYAgLlIJ6x66euaoncUuG4spw9tIg9t1UXXNoG3JY8r4tHVxEs_3AZVV_xBe98nN33N6a3To8jfXVzxZ0e1bprvz6-Fa7utqyrilrzbDsyWTthBqatAp3_7mL3c3b5ePySLp_vH66tFYoSYxwQzm-doM2FmKFMJCGCXGUJWSMjnIrVyOYTWs1QDGGGxLFJYloBayCxDcczOd183vn3rKERVu2CoqnRDbRcUDhAUUspiQMUONb4NwVOpNt7V2vcKQY3NqrX6bVaNzSoYRwyuy52LhgxbR14F46gxZJ0nE5Vt3b_-H-qZhHQ</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>Huang, Qing</creator><creator>Zhdanov, Renat</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20140901</creationdate><title>Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative</title><author>Huang, Qing ; Zhdanov, Renat</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-15d771d53c419290100db51058907632d9b016a42a00c3d1f820bf01a395513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Derivatives</topic><topic>Differential equations</topic><topic>Exact solutions</topic><topic>Fractional Harry-Dym equation</topic><topic>Group-invariant solution</topic><topic>Invariants</topic><topic>Lie symmetry</topic><topic>Mathematical analysis</topic><topic>Optimal system</topic><topic>Optimization</topic><topic>Riemann–Liouville derivative</topic><topic>Similarity</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Qing</creatorcontrib><creatorcontrib>Zhdanov, Renat</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physica A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Qing</au><au>Zhdanov, Renat</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative</atitle><jtitle>Physica A</jtitle><date>2014-09-01</date><risdate>2014</risdate><volume>409</volume><spage>110</spage><epage>118</epage><pages>110-118</pages><issn>0378-4371</issn><eissn>1873-2119</eissn><abstract>In this paper, group analysis of the time fractional Harry-Dym equation with Riemann–Liouville derivative is performed. Its maximal symmetry group in Lie’s sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equation under study are performed. As a result, the reduced fractional ordinary differential equations are deduced, and some group invariant solutions in explicit form are obtained as well.
•Lie classical method is used to investigate the time fractional Harry-Dym equation.•The maximal Lie symmetry group of the equation under study is derived.•Optimal system of subgroups are determined and the optimization of the system is proved.•Reduced fractional ODEs and some exact solutions in explicit forms are presented.•The approach used here can also be applied to other nonlinear fractional PDEs.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physa.2014.04.043</doi><tpages>9</tpages></addata></record> |
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| subjects | Derivatives Differential equations Exact solutions Fractional Harry-Dym equation Group-invariant solution Invariants Lie symmetry Mathematical analysis Optimal system Optimization Riemann–Liouville derivative Similarity Symmetry |
| title | Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative |
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