Abstract:

Based on the theory of the reproducing kernel, this paper constructed a new reproducing kernel space and the reproducing kernel function of the space is given by using the shifted Legendre polynomials as the basis function. It is different from former that this function is no longer a piecewise function, so when the fractional operator is used on the kernel function, the computation is reduced. Thus the approximate solution is more accurate. Finally, the numerical examples illustrate the validity of the method.

Key words: Fractional differential equations, Shifted Legendre polynomials, Reproducing kernel method