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Mathematical Problems in Engineering
Volume 2015, Article ID 902161, 10 pages
Research Article

Numerical Algorithm to Solve a Class of Variable Order Fractional Integral-Differential Equation Based on Chebyshev Polynomials

School of Aeronautic Science and Technology, Beihang University, Beijing 100191, China

Received 24 May 2015; Revised 30 August 2015; Accepted 31 August 2015

Academic Editor: Kishin Sadarangani

Copyright © 2015 Kangwen Sun and Ming Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is to study the Chebyshev polynomials for the solution of a class of variable order fractional integral-differential equation. The properties of Chebyshev polynomials together with the four kinds of operational matrixes of Chebyshev polynomials are used to reduce the problem to the solution of a system of algebraic equations. By solving the algebraic equations, the numerical solutions are acquired. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach and the results have been compared with the exact solution.