COMPARISON OF VARIOUS FRACTIONAL BASIS FUNCTIONS FOR SOLVING FRACTIONAL-ORDER LOGISTIC POPULATION MODEL

Mohammad Izadi

DOI Number
https://doi.org/10.22190/FUMI2004181I
First page
1181
Last page
1198

Abstract

Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value problem arising in population growth models. The method reduces the given problem to a set of algebraic equations consist of polynomial coefficients. Our main goal is to present a comparative study of these polynomials and to asses their performances and accuracies applied to the logistic population equation. Numerical applications are given to demonstrate the validity and applicability of the method. Comparisons are also made between the present method based on different basis functions and other existing approximation algorithms.

Keywords

Liouville-Caputo fractional derivative; Chebyshev and Chelyshkov polynomials; Collocation method; Logistic population model; Legendre polynomial.

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DOI: https://doi.org/10.22190/FUMI2004181I

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