A new solution method for nonlinear fractional integro-differential equations

Alkan S.

Discrete and Continuous Dynamical Systems - Series S, vol.8, no.6, pp.1065-1077, 2015 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 6
  • Publication Date: 2015
  • Doi Number: 10.3934/dcdss.2015.8.1065
  • Journal Name: Discrete and Continuous Dynamical Systems - Series S
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1065-1077
  • Keywords: Caputo derivative, Mathematica, Nonlinear fractional Fredholm integro-differential equation, Quadrature rule, Sinccollocation method
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

The aim of this paper is to obtain approximate solution of a class of nonlinear fractional Fredholm integro-differential equations by means of sinccollocation method which is not used for solving them in the literature before. The fractional derivatives are defined in the Caputo sense often used in fractional calculus. The important feature of the present study is that obtained results are stated as two new theorems. The introduced method is tested on some nonlinear problems and it seems that the method is a very efficient and powerful tool to obtain numerical solutions of nonlinear fractional integrodifferential equations.