Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system
In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi‐linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained vi...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2022-05, Vol.45 (7), p.3605-3623 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Shah, Firdous A. Irfan, Mohd Nisar, Kottakkaran S. |
| description | In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi‐linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained via block‐pulse functions. The obtained matrices are employed to transform the given time‐fractional population growth model into a non‐linear system of algebraic equations. Then, the quasi‐linearization technique is invoked to convert the underlying equations to a linear system of equations. The performance and accuracy of the proposed method is elucidated by a presenting a comparison with some numerical methods existing in the open literature. The numerical outcomes shows that the present method is more efficient than the existing ones. |
| doi_str_mv | 10.1002/mma.8006 |
| format | Article |
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The operational matrices of fractional order integration are obtained via block‐pulse functions. The obtained matrices are employed to transform the given time‐fractional population growth model into a non‐linear system of algebraic equations. Then, the quasi‐linearization technique is invoked to convert the underlying equations to a linear system of equations. The performance and accuracy of the proposed method is elucidated by a presenting a comparison with some numerical methods existing in the open literature. The numerical outcomes shows that the present method is more efficient than the existing ones.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.8006</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>collocation method ; Collocation methods ; fractional derivative ; Gegenbauer wavelet ; Growth models ; Linearization ; logistic equation ; Mathematical models ; Numerical methods ; operational matrices ; Population growth ; quasi‐linearization ; Volterra's population model</subject><ispartof>Mathematical methods in the applied sciences, 2022-05, Vol.45 (7), p.3605-3623</ispartof><rights>2021 John Wiley & Sons, Ltd.</rights><rights>2022 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2936-8928bc072a906e056f23b74f50b5420a8c54da0b43b55f3d57c66da3d1a753bd3</citedby><cites>FETCH-LOGICAL-c2936-8928bc072a906e056f23b74f50b5420a8c54da0b43b55f3d57c66da3d1a753bd3</cites><orcidid>0000-0001-8461-869X ; 0000-0001-5769-4320 ; 0000-0002-9088-123X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.8006$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.8006$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Shah, Firdous A.</creatorcontrib><creatorcontrib>Irfan, Mohd</creatorcontrib><creatorcontrib>Nisar, Kottakkaran S.</creatorcontrib><title>Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system</title><title>Mathematical methods in the applied sciences</title><description>In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi‐linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained via block‐pulse functions. The obtained matrices are employed to transform the given time‐fractional population growth model into a non‐linear system of algebraic equations. Then, the quasi‐linearization technique is invoked to convert the underlying equations to a linear system of equations. The performance and accuracy of the proposed method is elucidated by a presenting a comparison with some numerical methods existing in the open literature. The numerical outcomes shows that the present method is more efficient than the existing ones.</description><subject>collocation method</subject><subject>Collocation methods</subject><subject>fractional derivative</subject><subject>Gegenbauer wavelet</subject><subject>Growth models</subject><subject>Linearization</subject><subject>logistic equation</subject><subject>Mathematical models</subject><subject>Numerical methods</subject><subject>operational matrices</subject><subject>Population growth</subject><subject>quasi‐linearization</subject><subject>Volterra's population model</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp10LFOwzAQgGELgUQpSDyCJRaWlLMdO8lYVVCQWrHAHF0Sp03lxK2dtCoTj8Az8iSkhJXphvt0Ov2E3DKYMAD-UNc4iQHUGRkxSJKAhZE6JyNgEQQhZ-ElufJ-AwAxY3xEdnO90k2GnXb0gHttdEt3Hfrq-_PLVI1GV31gW9mG1rpd24KW1lFvzb5qVrR0mJ92aOjWbjszwJWzh3ZNa1toQ6uGIs2N9bqg_uhbXV-TixKN1zd_c0zenx7fZs_B4nX-MpsugpwnQgVxwuMsh4hjAkqDVCUXWRSWEjIZcsA4l2GBkIUik7IUhYxypQoUBcNIiqwQY3I33N06u-u0b9ON7Vz_q0-5CpUSjCdRr-4HlTvrvdNlunVVje6YMkhPQdM-aHoK2tNgoIfK6OO_Ll0up7_-B0r6eZg</recordid><startdate>20220515</startdate><enddate>20220515</enddate><creator>Shah, Firdous A.</creator><creator>Irfan, Mohd</creator><creator>Nisar, Kottakkaran S.</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0001-8461-869X</orcidid><orcidid>https://orcid.org/0000-0001-5769-4320</orcidid><orcidid>https://orcid.org/0000-0002-9088-123X</orcidid></search><sort><creationdate>20220515</creationdate><title>Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system</title><author>Shah, Firdous A. ; Irfan, Mohd ; Nisar, Kottakkaran S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2936-8928bc072a906e056f23b74f50b5420a8c54da0b43b55f3d57c66da3d1a753bd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>collocation method</topic><topic>Collocation methods</topic><topic>fractional derivative</topic><topic>Gegenbauer wavelet</topic><topic>Growth models</topic><topic>Linearization</topic><topic>logistic equation</topic><topic>Mathematical models</topic><topic>Numerical methods</topic><topic>operational matrices</topic><topic>Population growth</topic><topic>quasi‐linearization</topic><topic>Volterra's population model</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shah, Firdous A.</creatorcontrib><creatorcontrib>Irfan, Mohd</creatorcontrib><creatorcontrib>Nisar, Kottakkaran S.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shah, Firdous A.</au><au>Irfan, Mohd</au><au>Nisar, Kottakkaran S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2022-05-15</date><risdate>2022</risdate><volume>45</volume><issue>7</issue><spage>3605</spage><epage>3623</epage><pages>3605-3623</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi‐linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained via block‐pulse functions. The obtained matrices are employed to transform the given time‐fractional population growth model into a non‐linear system of algebraic equations. Then, the quasi‐linearization technique is invoked to convert the underlying equations to a linear system of equations. The performance and accuracy of the proposed method is elucidated by a presenting a comparison with some numerical methods existing in the open literature. The numerical outcomes shows that the present method is more efficient than the existing ones.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.8006</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0001-8461-869X</orcidid><orcidid>https://orcid.org/0000-0001-5769-4320</orcidid><orcidid>https://orcid.org/0000-0002-9088-123X</orcidid></addata></record> |
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| subjects | collocation method Collocation methods fractional derivative Gegenbauer wavelet Growth models Linearization logistic equation Mathematical models Numerical methods operational matrices Population growth quasi‐linearization Volterra's population model |
| title | Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system |
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