Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

作者：Yin, Fukang^*; Song, Junqiang; Wu, Yongwen; Zhang, Lilun

来源：Abstract and Applied Analysis, 2013, 2013: 562140.

DOI：10.1155/2013/562140

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.

• 出版日期2013
• 单位中国人民解放军国防科学技术大学