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Article

Analytical Solution of Nonlinear Fractional Volterra Population Growth Model Using the Modified Residual Power Series Method

by
Patcharee Dunnimit
1,
Araya Wiwatwanich
1 and
Duangkamol Poltem
1,2,*
1
Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
2
Centre of Excellence in Mathematics, Commission on Higher Education, Ministry of Education, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(11), 1779; https://doi.org/10.3390/sym12111779
Submission received: 1 October 2020 / Revised: 14 October 2020 / Accepted: 23 October 2020 / Published: 27 October 2020
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications)
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Abstract

In this paper, we introduce an analytical approximate solution of nonlinear fractional Volterra population growth model based on the Caputo fractional derivative and the Riemann fractional integral of the symmetry order. The residual power series method and Adomain decomposition method are implemented to find an approximate solution of this problem. The convergence analysis of the proposed technique has been proved. A numerical example is given to illustrate the method.
Keywords: fractional differential equations; population growth model; fractional power series; residual power series method fractional differential equations; population growth model; fractional power series; residual power series method

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MDPI and ACS Style

Dunnimit, P.; Wiwatwanich, A.; Poltem, D. Analytical Solution of Nonlinear Fractional Volterra Population Growth Model Using the Modified Residual Power Series Method. Symmetry 2020, 12, 1779. https://doi.org/10.3390/sym12111779

AMA Style

Dunnimit P, Wiwatwanich A, Poltem D. Analytical Solution of Nonlinear Fractional Volterra Population Growth Model Using the Modified Residual Power Series Method. Symmetry. 2020; 12(11):1779. https://doi.org/10.3390/sym12111779

Chicago/Turabian Style

Dunnimit, Patcharee, Araya Wiwatwanich, and Duangkamol Poltem. 2020. "Analytical Solution of Nonlinear Fractional Volterra Population Growth Model Using the Modified Residual Power Series Method" Symmetry 12, no. 11: 1779. https://doi.org/10.3390/sym12111779

APA Style

Dunnimit, P., Wiwatwanich, A., & Poltem, D. (2020). Analytical Solution of Nonlinear Fractional Volterra Population Growth Model Using the Modified Residual Power Series Method. Symmetry, 12(11), 1779. https://doi.org/10.3390/sym12111779

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