New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM
In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial d...
Gespeichert in:
| Veröffentlicht in: | Advances in difference equations 2016-09, Vol.2016 (1), p.1-19, Article 235 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 19 |
|---|---|
| container_issue | 1 |
| container_start_page | 1 |
| container_title | Advances in difference equations |
| container_volume | 2016 |
| creator | Rawashdeh, Mahmoud S Al-Jammal, Hadeel |
| description | In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed. |
| doi_str_mv | 10.1186/s13662-016-0960-x |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1845807528</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1845807528</sourcerecordid><originalsourceid>FETCH-LOGICAL-c392t-4dc87f388922968733bfea90f71c05d6238ed83505bb44f1c06b30e6347bdcdf3</originalsourceid><addsrcrecordid>eNp1kD1PwzAQhi0EEqXwA9gssbAE_JE4zogKBaRSFpgtJzmXVKnd2olo_z0OYUBITPbZz726exC6pOSGUiluA-VCsIRQkZBCkGR_hCZUyDyhMs2Pf91P0VkIa0JYkUo5QeslfGK93Xq3bza6Axxc23eNswF3Dhuvq6HQLbbOto0F7XE4hA42ATuDt9p3TfysG2PAg_0uYNfrMaEPjV3h7gPwfHn_co5OjG4DXPycU_Q-f3ibPSWL18fn2d0iqXjBuiStK5kbLmXBWBGn5rw0oAticlqRrBaMS6glz0hWlmlq4qMoOQHB07ysq9rwKboec-NSux5CpzZNqKBttQXXBxUtZJLkGZMRvfqDrl3v47oDFbWSlIsiUnSkKu9C8GDU1kdZ_qAoUYN9NdpX0b4a7Kt97GFjT4isXYH_lfxv0xcXfIl5</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1818604369</pqid></control><display><type>article</type><title>New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM</title><source>DOAJ Directory of Open Access Journals</source><source>EZB Electronic Journals Library</source><creator>Rawashdeh, Mahmoud S ; Al-Jammal, Hadeel</creator><creatorcontrib>Rawashdeh, Mahmoud S ; Al-Jammal, Hadeel</creatorcontrib><description>In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed.</description><identifier>ISSN: 1687-1847</identifier><identifier>ISSN: 1687-1839</identifier><identifier>EISSN: 1687-1847</identifier><identifier>DOI: 10.1186/s13662-016-0960-x</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Approximation ; Difference and Functional Equations ; Dynamical systems ; Exact solutions ; Functional Analysis ; Mathematical analysis ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Ordinary Differential Equations ; Partial Differential Equations ; Systems analysis</subject><ispartof>Advances in difference equations, 2016-09, Vol.2016 (1), p.1-19, Article 235</ispartof><rights>Rawashdeh and Al-Jammal 2016</rights><rights>The Author(s) 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c392t-4dc87f388922968733bfea90f71c05d6238ed83505bb44f1c06b30e6347bdcdf3</citedby><cites>FETCH-LOGICAL-c392t-4dc87f388922968733bfea90f71c05d6238ed83505bb44f1c06b30e6347bdcdf3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,864,27924,27925</link.rule.ids></links><search><creatorcontrib>Rawashdeh, Mahmoud S</creatorcontrib><creatorcontrib>Al-Jammal, Hadeel</creatorcontrib><title>New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM</title><title>Advances in difference equations</title><addtitle>Adv Differ Equ</addtitle><description>In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed.</description><subject>Analysis</subject><subject>Approximation</subject><subject>Difference and Functional Equations</subject><subject>Dynamical systems</subject><subject>Exact solutions</subject><subject>Functional Analysis</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Systems analysis</subject><issn>1687-1847</issn><issn>1687-1839</issn><issn>1687-1847</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kD1PwzAQhi0EEqXwA9gssbAE_JE4zogKBaRSFpgtJzmXVKnd2olo_z0OYUBITPbZz726exC6pOSGUiluA-VCsIRQkZBCkGR_hCZUyDyhMs2Pf91P0VkIa0JYkUo5QeslfGK93Xq3bza6Axxc23eNswF3Dhuvq6HQLbbOto0F7XE4hA42ATuDt9p3TfysG2PAg_0uYNfrMaEPjV3h7gPwfHn_co5OjG4DXPycU_Q-f3ibPSWL18fn2d0iqXjBuiStK5kbLmXBWBGn5rw0oAticlqRrBaMS6glz0hWlmlq4qMoOQHB07ysq9rwKboec-NSux5CpzZNqKBttQXXBxUtZJLkGZMRvfqDrl3v47oDFbWSlIsiUnSkKu9C8GDU1kdZ_qAoUYN9NdpX0b4a7Kt97GFjT4isXYH_lfxv0xcXfIl5</recordid><startdate>20160913</startdate><enddate>20160913</enddate><creator>Rawashdeh, Mahmoud S</creator><creator>Al-Jammal, Hadeel</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</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>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</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><scope>Q9U</scope></search><sort><creationdate>20160913</creationdate><title>New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM</title><author>Rawashdeh, Mahmoud S ; Al-Jammal, Hadeel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c392t-4dc87f388922968733bfea90f71c05d6238ed83505bb44f1c06b30e6347bdcdf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Analysis</topic><topic>Approximation</topic><topic>Difference and Functional Equations</topic><topic>Dynamical systems</topic><topic>Exact solutions</topic><topic>Functional Analysis</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Systems analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rawashdeh, Mahmoud S</creatorcontrib><creatorcontrib>Al-Jammal, Hadeel</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</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>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest - 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><collection>ProQuest Central Basic</collection><jtitle>Advances in difference equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rawashdeh, Mahmoud S</au><au>Al-Jammal, Hadeel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM</atitle><jtitle>Advances in difference equations</jtitle><stitle>Adv Differ Equ</stitle><date>2016-09-13</date><risdate>2016</risdate><volume>2016</volume><issue>1</issue><spage>1</spage><epage>19</epage><pages>1-19</pages><artnum>235</artnum><issn>1687-1847</issn><issn>1687-1839</issn><eissn>1687-1847</eissn><abstract>In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13662-016-0960-x</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1687-1847 |
| ispartof | Advances in difference equations, 2016-09, Vol.2016 (1), p.1-19, Article 235 |
| issn | 1687-1847 1687-1839 1687-1847 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1845807528 |
| source | DOAJ Directory of Open Access Journals; EZB Electronic Journals Library |
| subjects | Analysis Approximation Difference and Functional Equations Dynamical systems Exact solutions Functional Analysis Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Nonlinearity Ordinary Differential Equations Partial Differential Equations Systems analysis |
| title | New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T08%3A47%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=New%20approximate%20solutions%20to%20fractional%20nonlinear%20systems%20of%20partial%20differential%20equations%20using%20the%20FNDM&rft.jtitle=Advances%20in%20difference%20equations&rft.au=Rawashdeh,%20Mahmoud%20S&rft.date=2016-09-13&rft.volume=2016&rft.issue=1&rft.spage=1&rft.epage=19&rft.pages=1-19&rft.artnum=235&rft.issn=1687-1847&rft.eissn=1687-1847&rft_id=info:doi/10.1186/s13662-016-0960-x&rft_dat=%3Cproquest_cross%3E1845807528%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1818604369&rft_id=info:pmid/&rfr_iscdi=true |