Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions

In this paper, a new method based on the Legendre wavelets expansion together with operational matrices of fractional integration and derivative of these basis functions is proposed to solve fractional partial differential equations with Dirichlet boundary conditions. The proposed method is very convenient for solving such boundary value problems, since the boundary conditions are taken into account automatically. Convergence of the two-dimensional Legendre wavelets expansion is investigated. Illustrative examples are included to demonstrate the validity and applicability of the presented wavelets method.