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Mathematical Problems in Engineering
Volume 2017, Article ID 7853839, 13 pages
https://doi.org/10.1155/2017/7853839
Research Article

New Solutions for System of Fractional Integro-Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method

1Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, Egypt
2Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

Correspondence should be addressed to Hassan A. Zedan; moc.oohay@3002nadeznassah

Received 14 September 2016; Accepted 14 February 2017; Published 30 March 2017

Academic Editor: J.-C. Cortés

Copyright © 2017 Hassan A. Zedan et al. 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.

Abstract

Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro-differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numerical results with comparisons are made to confirm the reliability of the method. Chebyshev spectral method may be considered as alternative and efficient technique for finding the approximation of system of fractional integro-differential equations and Abel’s integral equations.