A collocation method for numerical solutions of fractional-order logistic population model

YÜZBAŞI Ş.

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, vol.9, no.2, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1142/s1793524516500315
  • Journal Name: INTERNATIONAL JOURNAL OF BIOMATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Fractional-order logistic population model, fractional derivative, Bessel functions of first kind, collocation method, approximate solution, nonlinear fractional differential equations, EQUATIONS, APPROXIMATIONS, INFECTION
  • Akdeniz University Affiliated: Yes

Abstract

In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.