TY - JOUR A2 - Ray, Santanu Saha AU - Yin, Fukang AU - Song, Junqiang AU - Wu, Yongwen AU - Zhang, Lilun PY - 2013 DA - 2013/11/18 TI - Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions SP - 562140 VL - 2013 AB - 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. SN - 1085-3375 UR - https://doi.org/10.1155/2013/562140 DO - 10.1155/2013/562140 JF - Abstract and Applied Analysis PB - Hindawi Publishing Corporation KW - ER -