Research Article Solving Fractional Partial Differential Equations with Corrected Fourier Series Method Nor Hafizah Zainal 1 and Adem KJlJçman 1,2 1 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia 2 Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia Correspondence should be addressed to Adem Kılıc ¸man; akilic@upm.edu.my Received 31 March 2014; Accepted 5 May 2014; Published 26 May 2014 Academic Editor: Hassan Eltayeb Copyright © 2014 N. H. Zainal and A. Kılıc ¸man. Tis 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. Te corrected Fourier series (CFS) is proposed for solving partial diferential equations (PDEs) with fractional time derivative on a fnite domain. In the previous work, we have been solving partial diferential equations by using corrected Fourier series. Te fractional derivatives are described in Riemann sense. Some numerical examples are presented to show the solutions. 1. Introduction In recent years, diferential equations of fractional orders have been appearing more and more frequently in various research and applications in the fuid mechanics, viscoelasticity, biol- ogy, physics, and engineering; see [1, 2]. Tere are some meth- ods usually used in solving the fractional partial diferential equations such as Laplace and Fourier transform, variational iteration method, and diferential transform methods. In this study, we want to use the corrected Fourier series method in solving the problems. In [3], corrected Fourier series method has been used in solving classical PDEs problems. Te corrected Fourier series is a combination of the uniformly convergent Fourier series and the correction functions and consists of algebraic polynomials and Heaviside step function. 2. Basic Definitions Te Riemann-Liouville fractional integral is the most popular defnition that we always fnd in the study of fractional calculus. Defnition 1. Te Riemann-Liouville fractional integral oper- ator of order >0 of a function () is defned as    () = 1 Γ () ∫  0 ( − ) −1  () . (1) Jumarie’s modifed Riemann-Liouville derivative of order  is defned by the following defnition. Defnition 2. Let : R → R,  → () denote a continuous function. Its fractional derivative of order  is defned as follows: for <0,    = 1 Γ (−) ∫  0 ( − ) −−1 ( () −  (0)) , (2) for >0,    = 1 Γ (1 − )   ∫  0 ( − ) − ( () −  (0)) , where 0 <  < 1, 0     () = 1 Γ ( − )     ∫  0 ( − ) −−1 [ () −  (0)] , (3) where −1<< with ∈. Defnition 3 (see [4–7]). Fractional derivative of com- pounded function is defned as    ≅ Γ (1 + ) , 0 <  < 1. (4) Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014, Article ID 958931, 5 pages http://dx.doi.org/10.1155/2014/958931