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Journal of Function Spaces
Volume 2018, Article ID 3152502, 10 pages
Research Article

Approximating Solution of Fabrizio-Caputo Volterra’s Model for Population Growth in a Closed System by Homotopy Analysis Method

1Department of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran
2Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Correspondence should be addressed to Juan J. Nieto; se.csu@gior.otein.esojnauj

Received 23 March 2017; Revised 20 September 2017; Accepted 28 September 2017; Published 11 January 2018

Academic Editor: Xinguang Zhang

Copyright © 2018 Tahereh Bashiri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 of identical individuals to show crowding and sensitivity to “total metabolism”: 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: , , subject to the initial condition . 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.