Abstract: Fractional partial differential equations are regarded as one kind of common differ-ential equations to describe the engineering problems. Compared with other traditional methods, the proposed method has a great advantage on computational precision and efficiency. Legendre function method expands the dual functions as basis functions, and transforms the original equations into a system of algebra equations combined with the operational matrices. This paper introduces the method which can accurately stimulate the complex mathematical phenomenon of the engineering problems, and is relatively simple in the function construction and theoretical derivation. Finally, the error analysis is presented to verify the effectiveness and robust.

Key words: Legendre functions, operational matrix, fractional partial differential equations, numerical solution, Tau method