Application of tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model
Based on the tan ( Φ ( ξ ) / 2 ) -expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences, India, Section A, physical sciences India, Section A, physical sciences, 2020, Vol.90 (1), p.67-86 |
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| container_title | Proceedings of the National Academy of Sciences, India, Section A, physical sciences |
| container_volume | 90 |
| creator | Manafian, Jalil Farshbaf Zinati, Reza |
| description | Based on the
tan
(
Φ
(
ξ
)
/
2
)
-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions. |
| doi_str_mv | 10.1007/s40010-018-0550-2 |
| format | Article |
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tan
(
Φ
(
ξ
)
/
2
)
-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions.</description><identifier>ISSN: 0369-8203</identifier><identifier>EISSN: 2250-1762</identifier><identifier>DOI: 10.1007/s40010-018-0550-2</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Applied and Technical Physics ; Atomic ; Differential equations ; Exact solutions ; Hyperbolic functions ; Mathematical models ; Molecular ; Nonlinear equations ; Optical and Plasma Physics ; Ordinary differential equations ; Physics ; Physics and Astronomy ; Quantum Physics ; Rational functions ; Research Article ; Trigonometric functions</subject><ispartof>Proceedings of the National Academy of Sciences, India, Section A, physical sciences, 2020, Vol.90 (1), p.67-86</ispartof><rights>The National Academy of Sciences, India 2018</rights><rights>2018© The National Academy of Sciences, India 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p1412-cd1c91c2a5789ebf070d43c69a09c0e0d469720fecf7fe4c661723f6d4d301013</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40010-018-0550-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40010-018-0550-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Manafian, Jalil</creatorcontrib><creatorcontrib>Farshbaf Zinati, Reza</creatorcontrib><title>Application of tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model</title><title>Proceedings of the National Academy of Sciences, India, Section A, physical sciences</title><addtitle>Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci</addtitle><description>Based on the
tan
(
Φ
(
ξ
)
/
2
)
-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions.</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Differential equations</subject><subject>Exact solutions</subject><subject>Hyperbolic functions</subject><subject>Mathematical models</subject><subject>Molecular</subject><subject>Nonlinear equations</subject><subject>Optical and Plasma Physics</subject><subject>Ordinary differential equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Rational functions</subject><subject>Research Article</subject><subject>Trigonometric functions</subject><issn>0369-8203</issn><issn>2250-1762</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkM9KAzEQxoMoWLQP4C3gpT3ETpLdZHMsxX9Q8KLnJWYTuyVN1s1W9IV8DB-hz2SWCuYwmWG--Zj5IXRF4YYCyEUqACgQoBWBsgTCTtCEsZxQKdgpmgAXilQM-DmaprSF_EqpmCgmqF52nW-NHtoYcHR40GF2-J4dfuYLNif2s9Mhja2dHTaxwUPEKfoPm-PO4hCDb4PVPXa9NqOF9rjbfKVs6PEuNtZfojOnfbLTv_8CvdzdPq8eyPrp_nG1XJOOFpQR01CjqGG6lJWyrw4kNAU3QmlQBmwuhJIMnDVOOlsYIahk3ImmaHg-nfILdH307fr4vrdpqLdx3-d9Us24qIQoleBZxY6q1PVteLP9v4pCPbKsjyzrzLIeWebpX_UJZ84</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Manafian, Jalil</creator><creator>Farshbaf Zinati, Reza</creator><general>Springer India</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2020</creationdate><title>Application of tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model</title><author>Manafian, Jalil ; Farshbaf Zinati, Reza</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1412-cd1c91c2a5789ebf070d43c69a09c0e0d469720fecf7fe4c661723f6d4d301013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Differential equations</topic><topic>Exact solutions</topic><topic>Hyperbolic functions</topic><topic>Mathematical models</topic><topic>Molecular</topic><topic>Nonlinear equations</topic><topic>Optical and Plasma Physics</topic><topic>Ordinary differential equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Rational functions</topic><topic>Research Article</topic><topic>Trigonometric functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Manafian, Jalil</creatorcontrib><creatorcontrib>Farshbaf Zinati, Reza</creatorcontrib><jtitle>Proceedings of the National Academy of Sciences, India, Section A, physical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Manafian, Jalil</au><au>Farshbaf Zinati, Reza</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Application of tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model</atitle><jtitle>Proceedings of the National Academy of Sciences, India, Section A, physical sciences</jtitle><stitle>Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci</stitle><date>2020</date><risdate>2020</risdate><volume>90</volume><issue>1</issue><spage>67</spage><epage>86</epage><pages>67-86</pages><issn>0369-8203</issn><eissn>2250-1762</eissn><abstract>Based on the
tan
(
Φ
(
ξ
)
/
2
)
-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s40010-018-0550-2</doi><tpages>20</tpages></addata></record> |
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| identifier | ISSN: 0369-8203 |
| ispartof | Proceedings of the National Academy of Sciences, India, Section A, physical sciences, 2020, Vol.90 (1), p.67-86 |
| issn | 0369-8203 2250-1762 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Applied and Technical Physics Atomic Differential equations Exact solutions Hyperbolic functions Mathematical models Molecular Nonlinear equations Optical and Plasma Physics Ordinary differential equations Physics Physics and Astronomy Quantum Physics Rational functions Research Article Trigonometric functions |
| title | Application of tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model |
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