Approximating Solution of Fabrizio-Caputo Volterra's Model for Population Growth in a Closed System by Homotopy Analysis Method. (11th January 2018)

• Record Type: Journal Article
• Authors: Bashiri, Tahereh; Vaezpour, S. Mansour; Nieto, Juan J.
• Other Names: Zhang Xinguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2018(2018)
• Publication Date: 2018-01-11
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2018/3152502
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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 populationu ( t ) of identical individuals to show crowding and sensitivity to "total metabolism":d u / d t = a u ( t ) - b u 2 ( t ) - c u ( t ) ∫ 0 t u ( s ) d s . 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: C F D α u ( t ) = a u ( t ) - b u 2 ( t ) - c u ( t ) ∫ 0 t u ( s ) d s, α ∈ [ 0, 1 ], subject to the initial conditionu ( 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.