A New Finite Element Analysis for Inhomogeneous Boundary-Value Problems of Space Fractional Differential Equations

In this paper the framework and convergence analysis of finite element methods (FEMs) for space fractional differential equations (FDEs) with inhomogeneous boundary conditions are studied. Since the traditional framework of Gakerkin methods for space FDEs with homogeneous boundary conditions is not true any more for the case of inhomogeneous boundary conditions, this paper develops a technique by introducing a new fractional derivative space in which the Galerkin method works and proves the convergence rates of the FEMs.