Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions. (18th November 2013)

• Record Type: Journal Article
• Authors: Yin, Fukang; Song, Junqiang; Wu, Yongwen; Zhang, Lilun
• Other Names: Ray Santanu Saha Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-11-18
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/562140
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.