Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method
•We applied HPM for solving time-fractional PDEs with proportional delay.•Convergence theorem of method and maximum truncation error are given.•Some examples are solved by HPM. In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with...
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| Veröffentlicht in: | Applied mathematical modelling 2016-07, Vol.40 (13-14), p.6639-6649 |
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| creator | Sakar, Mehmet Giyas Uludag, Fatih Erdogan, Fevzi |
| description | •We applied HPM for solving time-fractional PDEs with proportional delay.•Convergence theorem of method and maximum truncation error are given.•Some examples are solved by HPM.
In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of α are presented graphically. |
| doi_str_mv | 10.1016/j.apm.2016.02.005 |
| format | Article |
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In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of α are presented graphically.</description><identifier>ISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2016.02.005</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Caputo derivative ; Delay ; Derivatives ; Fractional partial differential equation ; Homotopy perturbation method ; Linearization ; Mathematical models ; Nonlinearity ; Partial differential equations ; Perturbation methods ; Proportional delay</subject><ispartof>Applied mathematical modelling, 2016-07, Vol.40 (13-14), p.6639-6649</ispartof><rights>2016 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c443t-79aa258fb435f5653dbc6fce56fda139da8f5a68f83a8c90ca865dbb4b854dc43</citedby><cites>FETCH-LOGICAL-c443t-79aa258fb435f5653dbc6fce56fda139da8f5a68f83a8c90ca865dbb4b854dc43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0307904X16300695$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Sakar, Mehmet Giyas</creatorcontrib><creatorcontrib>Uludag, Fatih</creatorcontrib><creatorcontrib>Erdogan, Fevzi</creatorcontrib><title>Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method</title><title>Applied mathematical modelling</title><description>•We applied HPM for solving time-fractional PDEs with proportional delay.•Convergence theorem of method and maximum truncation error are given.•Some examples are solved by HPM.
In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of α are presented graphically.</description><subject>Caputo derivative</subject><subject>Delay</subject><subject>Derivatives</subject><subject>Fractional partial differential equation</subject><subject>Homotopy perturbation method</subject><subject>Linearization</subject><subject>Mathematical models</subject><subject>Nonlinearity</subject><subject>Partial differential equations</subject><subject>Perturbation methods</subject><subject>Proportional delay</subject><issn>0307-904X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9UD1PwzAQzQASpfAD2DyyJDiJnTpiQqV8SBUwgMRmOfZZdZXEwXZA-fc4tDPT3b177-nuJclVjrMc59XNPhNDlxWxzXCRYUxPkgUu8SqtMfk8S8693-OIxmmRdC9jB85I0SJv2zEY2yOrUTAdpNoJOQNx19u-NT0Ih97uNx79mLBDg7ODdUeCglZMHjUT2tnOBjtMaAAXRteIP88Ows6qi-RUi9bD5bEuk4-Hzfv6Kd2-Pj6v77apJKQM6aoWoqBMN6Skmla0VI2stARaaSXyslaCaSoqplkpmKyxFKyiqmlIwyhRkpTL5PrgG2_8GsEH3hkvoW1FD3b0PGcFJauckpmaH6jSWe8daD440wk38RzzOU6-5zFOPsfJccFjcFFze9BA_OHbgONeGuglKONABq6s-Uf9C2Ojgyo</recordid><startdate>201607</startdate><enddate>201607</enddate><creator>Sakar, Mehmet Giyas</creator><creator>Uludag, Fatih</creator><creator>Erdogan, Fevzi</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201607</creationdate><title>Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method</title><author>Sakar, Mehmet Giyas ; Uludag, Fatih ; Erdogan, Fevzi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c443t-79aa258fb435f5653dbc6fce56fda139da8f5a68f83a8c90ca865dbb4b854dc43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Caputo derivative</topic><topic>Delay</topic><topic>Derivatives</topic><topic>Fractional partial differential equation</topic><topic>Homotopy perturbation method</topic><topic>Linearization</topic><topic>Mathematical models</topic><topic>Nonlinearity</topic><topic>Partial differential equations</topic><topic>Perturbation methods</topic><topic>Proportional delay</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sakar, Mehmet Giyas</creatorcontrib><creatorcontrib>Uludag, Fatih</creatorcontrib><creatorcontrib>Erdogan, Fevzi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science 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><jtitle>Applied mathematical modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sakar, Mehmet Giyas</au><au>Uludag, Fatih</au><au>Erdogan, Fevzi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method</atitle><jtitle>Applied mathematical modelling</jtitle><date>2016-07</date><risdate>2016</risdate><volume>40</volume><issue>13-14</issue><spage>6639</spage><epage>6649</epage><pages>6639-6649</pages><issn>0307-904X</issn><abstract>•We applied HPM for solving time-fractional PDEs with proportional delay.•Convergence theorem of method and maximum truncation error are given.•Some examples are solved by HPM.
In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of α are presented graphically.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2016.02.005</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Caputo derivative Delay Derivatives Fractional partial differential equation Homotopy perturbation method Linearization Mathematical models Nonlinearity Partial differential equations Perturbation methods Proportional delay |
| title | Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method |
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