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Numerical methods for solving space fractional partial differential equations by using Hadamard finitepart integral approachWe introduce a novel numerical method for solving twosided space fractional partial differential equation in two dimensional case. The approximation of the space fractional RiemannLiouville derivative is based on the approximation of the Hadamard finitepart integral which has the convergence order $O(h^{3 \alpha})$, where $h$ is the space step size and $\alpha\in (1, 2)$ is the order of RiemannLiouville fractional derivative. Based on this scheme, we introduce a shifted finite difference method for solving space fractional partial differential equation. We obtained the error estimates with the convergence orders $O(\tau +h^{3\alpha}+ h^{\beta})$, where $\tau$ is the time step size and $\beta >0$ is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation. Unlike the numerical methods for solving space fractional partial differential equation constructed by using the standard shifted Gr\"unwaldLetnikov formula or higher order Lubich'e methods which require the solution of the equation satisfies the homogeneous Dirichlet boundary condition in order to get the first order convergence, the numerical method for solving space fractional partial differential equation constructed by using Hadamard finitepart integral approach does not require the solution of the equation satisfies the Dirichlet homogeneous boundary condition. Numerical results show that the experimentally determined convergence order obtained by using the Hadamard finitepart integral approach for solving space fractional partial differential equation with nonhomogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained by using the numerical methods constructed with the standard shifted Gr\"unwaldLetnikov formula or Lubich's higer order approximation schemes.