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Abstract and Applied Analysis
Volume 2014, Article ID 626275, 8 pages
Research Article

New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia
2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Received 19 March 2014; Accepted 29 April 2014; Published 22 May 2014

Academic Editor: Ali H. Bhrawy

Copyright © 2014 W. M. Abd-Elhameed and Y. H. Youssri. 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.


We introduce two new spectral wavelets algorithms for solving linear and nonlinear fractional-order Riccati differential equation. The suggested algorithms are basically based on employing the ultraspherical wavelets together with the tau and collocation spectral methods. The main idea for obtaining spectral numerical solutions depends on converting the differential equation with its initial condition into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. For the sake of illustrating the efficiency and the applicability of our algorithms, some numerical examples including comparisons with some algorithms in the literature are presented.