A new solution method for nonlinear fractional integro-differential equations

Sertan  Alkan

doi:10.3934/dcdss.2015.8.1065

Article Contents

2015, Volume 8, Issue 6: 1065-1077. Doi: 10.3934/dcdss.2015.8.1065

This issue Previous Article Reproducing kernel functions for difference equations Next Article A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions

A new solution method for nonlinear fractional integro-differential equations

Sertan Alkan^1,

1.
Department of Mathematics, Mustafa Kemal University, 31000, Hatay

Received: April 2015

Revised: August 2015

Published: December 2015

Abstract / Introduction Related Papers Cited by

Abstract

The aim of this paper is to obtain approximate solution of a class of nonlinear fractional Fredholm integro-differential equations by means of sinc-collocation 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 integro-differential equations.

Keywords:

Nonlinear fractional Fredholm integro-differential equation,
sinc-collocation method,
Caputo derivative,
quadrature rule,
mathematica.

Mathematics Subject Classification: Primary: 41A55, 41A30; Secondary: 65D15, 65D32.

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