Legendre wavelets method for approximate solution of fractional-order differential equations under multi-point boundary conditions

In this paper, Legendre wavelet collocation method is applied for numerical solutions of the fractional-order differential equations subject to multi-point boundary conditions. The explicit formula of fractional integral of a single Legendre wavelet is derived from the definition by means of the shifted Legendre polynomial. The proposed method is very convenient for solving fractional-order multi-point boundary conditions, since the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces equations to those of solving a system of algebraic equations which greatly simplifies the problem. Several numerical examples are solved to demonstrate the validity and applicability of the presented method.