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International Journal of Differential Equations
Volume 2010 (2010), Article ID 968186, 13 pages
http://dx.doi.org/10.1155/2010/968186
Research Article

The Use of Fractional B-Splines Wavelets in Multiterms Fractional Ordinary Differential Equations

School of Mathematical and Computer Sciences, Fuzhou University, Fuzhou 350002, China

Received 31 July 2009; Revised 2 November 2009; Accepted 4 November 2009

Academic Editor: Fawang Liu

Copyright © 2010 X. Huang and X. Lu. 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

We discuss the existence and uniqueness of the solutions of the nonhomogeneous linear differential equations of arbitrary positive real order by using the fractional B-Splines wavelets and the Mittag-Leffler function. The differential operators are taken in the Riemann-Liouville sense and the initial values are zeros. The scheme of solving the fractional differential equations and the explicit expression of the solution is given in this paper. At last, we show the asymptotic solution of the differential equations of fractional order and corresponding truncated error in theory.