A numerical approximation for Volterra's population growth model with fractional order

YÜZBAŞI Ş.

APPLIED MATHEMATICAL MODELLING, cilt.37, sa.5, ss.3216-3227, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 5
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.apm.2012.07.041
  • Dergi Adı: APPLIED MATHEMATICAL MODELLING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3216-3227
  • Anahtar Kelimeler: Population dynamics, Fractional Volterra's population model, Fractional derivative, Bessel collocation method, Nonlinear integro-differential equations, COLLOCATION APPROACH, POLYNOMIAL SOLUTIONS, RATIONAL CHEBYSHEV, PADE APPROXIMANTS, EQUATIONS, SYSTEMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

This paper presents a numerical scheme for approximate solutions of the fractional Volterra's model for population growth of a species in a closed system. In fact, the Bessel collocation method is extended by using the time-fractional derivative in the Caputo sense to give solutions for the mentioned model problem. In this extended of the method, a generalization of the Bessel functions of the first kind is used and its matrix form is constructed. And then, the matrix form based on the collocation points is formed for the each term of this model problem. Hence, the method converts the model problem into a system of nonlinear algebraic equations. We give some numerical applications to show efficiency and accuracy of the method. In applications, the reliability of the technique is demonstrated by the error function based on accuracy of the approximate solution. (C) 2012 Elsevier Inc. All rights reserved.

This paper presents a numerical scheme for approximate solutions of the fractional Volterra’s model for population growth of a species in a closed system. In fact, the Bessel collocation method is extended by using the time-fractional derivative in the Caputo sense to give solutions for the mentioned model problem. In this extended of the method, a generalization of the Bessel functions of the first kind is used and its matrix form is constructed. And then, the matrix form based on the collocation points is formed for the each term of this model problem. Hence, the method converts the model problem into a system of nonlinear algebraic equations. We give some numerical applications to show efficiency and accuracy of the method. In applications, the reliability of the technique is demonstrated by the error function based on accuracy of the approximate solution.