Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model
This paper suggests two component homotopy method to solve nonlinear fractional integrodifferential equations, namely, Volterra's population model. Padé approximation was effectively used in this method to capture the essential behavior of solutions for the mathematical model of accumulated eff...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/845945 |
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| _version_ | 1832548667361329152 |
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| author | Najeeb Alam Khan Amir Mahmood Nadeem Alam Khan Asmat Ara |
| author_facet | Najeeb Alam Khan Amir Mahmood Nadeem Alam Khan Asmat Ara |
| author_sort | Najeeb Alam Khan |
| collection | DOAJ |
| description | This paper suggests two component homotopy method to solve nonlinear fractional integrodifferential equations, namely, Volterra's population model. Padé approximation was effectively used in this method to capture the essential behavior of solutions for the mathematical model of accumulated effect of toxins on a population living in a closed system. The behavior of the solutions and the effects of different values of fractional-order α are indicated graphically. The study outlines significant features of this method as well as sheds some light on advantages of the method over the other. The results show that this method is very efficient, convenient, and can be adapted to fit a larger class of problems. |
| format | Article |
| id | doaj-art-2f83831651944d108838c2c6d47fb258 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-2f83831651944d108838c2c6d47fb2582025-02-03T06:13:17ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/845945845945Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population ModelNajeeb Alam Khan0Amir Mahmood1Nadeem Alam Khan2Asmat Ara3Department of Mathematical Sciences, University of Karachi, Karachi 75270, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Lahore, PakistanDepartment of Mathematical Sciences, University of Karachi, Karachi 75270, PakistanDepartment of Mathematical Sciences, University of Karachi, Karachi 75270, PakistanThis paper suggests two component homotopy method to solve nonlinear fractional integrodifferential equations, namely, Volterra's population model. Padé approximation was effectively used in this method to capture the essential behavior of solutions for the mathematical model of accumulated effect of toxins on a population living in a closed system. The behavior of the solutions and the effects of different values of fractional-order α are indicated graphically. The study outlines significant features of this method as well as sheds some light on advantages of the method over the other. The results show that this method is very efficient, convenient, and can be adapted to fit a larger class of problems.http://dx.doi.org/10.1155/2012/845945 |
| spellingShingle | Najeeb Alam Khan Amir Mahmood Nadeem Alam Khan Asmat Ara Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model International Journal of Differential Equations |
| title | Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model |
| title_full | Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model |
| title_fullStr | Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model |
| title_full_unstemmed | Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model |
| title_short | Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model |
| title_sort | analytical study of nonlinear fractional order integrodifferential equation revisit volterra s population model |
| url | http://dx.doi.org/10.1155/2012/845945 |
| work_keys_str_mv | AT najeebalamkhan analyticalstudyofnonlinearfractionalorderintegrodifferentialequationrevisitvolterraspopulationmodel AT amirmahmood analyticalstudyofnonlinearfractionalorderintegrodifferentialequationrevisitvolterraspopulationmodel AT nadeemalamkhan analyticalstudyofnonlinearfractionalorderintegrodifferentialequationrevisitvolterraspopulationmodel AT asmatara analyticalstudyofnonlinearfractionalorderintegrodifferentialequationrevisitvolterraspopulationmodel |