Genocchi polynomial method for the multiterm variable-order fractional differential equations


TURAL POLAT S. N. , TURAN DİNCEL A.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.40, no.1, pp.79-84, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.14744/sigma.2021.00032
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index, Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.79-84
  • Keywords: Genocchi polynomials, Collocation method, Variable-order fractional differential equations, Numerical FDE solutions

Abstract

In this paper a numerical solution for multiterm varable-order fractional differential equations (VO-FDEs) using Genocchi polynomials is proffered. By making use of the Genocchi polynomials, a multiterm VO-FDE can be approximated by a corresponding system of algebraic equations. To be able to do that, operational matrices for variable order fractional differentials are obtained using Genocchi polynomials. Then the algebraic equation system is solved for the coefficient values, thus the approximate solution is obtained by using the linear combination of those coefficients. Numerical examples are provided.