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

YÜZBAŞI Ş.

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, cilt.9, sa.2, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s1793524516500315
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIOMATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Fractional-order logistic population model, fractional derivative, Bessel functions of first kind, collocation method, approximate solution, nonlinear fractional differential equations, EQUATIONS, APPROXIMATIONS, INFECTION
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.