Approximating Solution of Fabrizio-Caputo Volterra’s Model for Population Growth in a Closed System by Homotopy Analysis Method
Joint Authors
Nieto, Juan Jose
Bashiri, Tahereh
Vaezpour, S. Mansour
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-01-11
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Volterra’s model for population growth in a closed system consists in an integral term to indicate accumulated toxicity besides the usual terms of the logistic equation.
Scudo in 1971 suggested the Volterra model for a population u(t) of identical individuals to show crowding and sensitivity to “total metabolism”: du/dt=au(t)-bu2(t)-cu(t)∫0tu(s)ds.
In this paper our target is studying the existence and uniqueness as well as approximating the following Caputo-Fabrizio Volterra’s model for population growth in a closed system: CFDαu(t)=au(t)-bu2(t)-cu(t)∫0tu(s)ds, α∈[0,1], subject to the initial condition u(0)=0.
The mechanism for approximating the solution is Homotopy Analysis Method which is a semianalytical technique to solve nonlinear ordinary and partial differential equations.
Furthermore, we use the same method to analyze a similar closed system by considering classical Caputo’s fractional derivative.
Comparison between the results for these two factional derivatives is also included.
American Psychological Association (APA)
Bashiri, Tahereh& Vaezpour, S. Mansour& Nieto, Juan Jose. 2018. Approximating Solution of Fabrizio-Caputo Volterra’s Model for Population Growth in a Closed System by Homotopy Analysis Method. Journal of Function Spaces،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1185997
Modern Language Association (MLA)
Bashiri, Tahereh…[et al.]. Approximating Solution of Fabrizio-Caputo Volterra’s Model for Population Growth in a Closed System by Homotopy Analysis Method. Journal of Function Spaces No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1185997
American Medical Association (AMA)
Bashiri, Tahereh& Vaezpour, S. Mansour& Nieto, Juan Jose. Approximating Solution of Fabrizio-Caputo Volterra’s Model for Population Growth in a Closed System by Homotopy Analysis Method. Journal of Function Spaces. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1185997
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1185997