Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method
This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with i...
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| Veröffentlicht in: | Mathematical problems in engineering 2016-01, Vol.2016 (2016), p.1-15 |
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| container_title | Mathematical problems in engineering |
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| creator | Zhang, He Yang, Xue Gao, Yixian Xu, Fei |
| description | This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems in R n . Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2 n th-order time-space fractional Boussinesq equations in R and fourth-order time-space fractional Boussinesq equations in R 2 and R n . Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations. |
| doi_str_mv | 10.1155/2016/5492535 |
| format | Article |
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Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems in R n . Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2 n th-order time-space fractional Boussinesq equations in R and fourth-order time-space fractional Boussinesq equations in R 2 and R n . Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2016/5492535</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Approximation ; Boundary value problems ; Boussinesq equations ; Calculus ; Construction ; Differential equations ; Engineering ; Exact solutions ; Fractional calculus ; Initial value problems ; Mathematical models ; Mathematics ; Partial differential equations ; Power ; Power series ; Propagation ; Researchers ; Science ; Studies ; Water waves</subject><ispartof>Mathematical problems in engineering, 2016-01, Vol.2016 (2016), p.1-15</ispartof><rights>Copyright © 2016 Fei Xu et al.</rights><rights>Copyright © 2016 Fei Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c393t-f3f50bff0df08535c95295f74f9ec3488beaf3fbfd86dfcfa35ac854854e89ed3</citedby><cites>FETCH-LOGICAL-c393t-f3f50bff0df08535c95295f74f9ec3488beaf3fbfd86dfcfa35ac854854e89ed3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><contributor>Caponetto, Riccardo</contributor><creatorcontrib>Zhang, He</creatorcontrib><creatorcontrib>Yang, Xue</creatorcontrib><creatorcontrib>Gao, Yixian</creatorcontrib><creatorcontrib>Xu, Fei</creatorcontrib><title>Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method</title><title>Mathematical problems in engineering</title><description>This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). 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Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.</description><subject>Approximation</subject><subject>Boundary value problems</subject><subject>Boussinesq equations</subject><subject>Calculus</subject><subject>Construction</subject><subject>Differential equations</subject><subject>Engineering</subject><subject>Exact solutions</subject><subject>Fractional calculus</subject><subject>Initial value problems</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Partial differential equations</subject><subject>Power</subject><subject>Power series</subject><subject>Propagation</subject><subject>Researchers</subject><subject>Science</subject><subject>Studies</subject><subject>Water waves</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqF0VFLwzAQB_AgCs7pm88S8EXQuqRp1vRRx6bCRHEOfCtZenEZXbMlLcNvb2YHyl6EwB3HjyPHH6FzSm4p5bwXE9rv8SSLOeMHqEN5n0WcJulh6EmcRDRmH8foxPsFITHlVHTQZmArX7tG1cZW2Go8cvKnlyV-tRtweALOgMcTWzbbuce1_YvubeO9qcCv8XDdyJZMw-QTv4E3RbO_6BnquS1O0ZGWpYezXe2i6Wj4PniMxi8PT4O7caRYxupIM83JTGtSaCLCVSrjccZ1mugMFEuEmIEMZqYL0S-00pJxqQRPwgORQcG66Krdu3J23YCv86XxCspSVhB-nlMRBx04C_Ryjy5s48KNQaUZEzxNOQ_qplXKWe8d6HzlzFK6r5ySfJtCvk0h36UQ-HXL56Yq5Mb8py9aDcGAlr-ahuwYYd_zAJMc</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Zhang, He</creator><creator>Yang, Xue</creator><creator>Gao, Yixian</creator><creator>Xu, Fei</creator><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20160101</creationdate><title>Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method</title><author>Zhang, He ; Yang, Xue ; Gao, Yixian ; Xu, Fei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c393t-f3f50bff0df08535c95295f74f9ec3488beaf3fbfd86dfcfa35ac854854e89ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Approximation</topic><topic>Boundary value problems</topic><topic>Boussinesq equations</topic><topic>Calculus</topic><topic>Construction</topic><topic>Differential equations</topic><topic>Engineering</topic><topic>Exact solutions</topic><topic>Fractional calculus</topic><topic>Initial value problems</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Partial differential equations</topic><topic>Power</topic><topic>Power series</topic><topic>Propagation</topic><topic>Researchers</topic><topic>Science</topic><topic>Studies</topic><topic>Water waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, He</creatorcontrib><creatorcontrib>Yang, Xue</creatorcontrib><creatorcontrib>Gao, Yixian</creatorcontrib><creatorcontrib>Xu, Fei</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Engineering Database</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, He</au><au>Yang, Xue</au><au>Gao, Yixian</au><au>Xu, Fei</au><au>Caponetto, Riccardo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2016-01-01</date><risdate>2016</risdate><volume>2016</volume><issue>2016</issue><spage>1</spage><epage>15</epage><pages>1-15</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems in R n . Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2 n th-order time-space fractional Boussinesq equations in R and fourth-order time-space fractional Boussinesq equations in R 2 and R n . Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2016/5492535</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Approximation Boundary value problems Boussinesq equations Calculus Construction Differential equations Engineering Exact solutions Fractional calculus Initial value problems Mathematical models Mathematics Partial differential equations Power Power series Propagation Researchers Science Studies Water waves |
| title | Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method |
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