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Mathematical Problems in Engineering
Volume 2014, Article ID 140453, 11 pages
http://dx.doi.org/10.1155/2014/140453
Review Article

Wavelet Methods for Solving Fractional Order Differential Equations

Department of Mathematics, National Institute of Technology, Rourkela 769008, India

Received 14 February 2014; Accepted 23 April 2014; Published 27 May 2014

Academic Editor: Adem Kılıçman

Copyright © 2014 A. K. Gupta and S. Saha Ray. 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

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order.