In this article, a general type of two-dimensional time-fractional telegraph equation explained by the Caputo derivative sense for (1 < α ≤ 2) is considered and analyzed by a method based on the Galerkin weak form and local radial point interpolant (LRPI) approximation subject to given appropriate initial and Dirichlet boundary conditions. In the proposed method, so-called meshless local radial point interpolation (MLRPI) method, a meshless Galerkin weak form is applied to the interior nodes while the meshless collocation method is used for the nodes on the boundary, so the Dirichlet boundary condition is imposed directly. The point interpolation method is proposed to construct shape functions using the radial basis functions. In the MLRPI method, it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares. Two numerical examples are presented and satisfactory agreements are achieved.

The purpose of the current investigation is to determine numerical solution of time-fractional diffusion-wave equation with damping for Caputo's fractional derivative of orderα(1<α≤2). A meshless local radial point interpolation (MLRPI) scheme based on Galerkin weak form is analyzed. The reason of choosing MLRPI approach is that it dose not require any background integrations cells, instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape. The unconditional stability and convergence with order O(τ6−2α) are proved, where τ is time stepping. Also, Several numerical experiments are illustrated to verify theoretical analysis.

http://www.sciencedirect.com/science/article/pii/S0021999116000942

I am a Vahid Reza Hosseini PHD student in China. My major is mechanic and I am working on fractions and mesh method and meshless method. I have been looking for opprecunity study for 6 months or more. If you have a position for me,please let me know

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Abstract
In this paper, we implement the radial basis functions for solving a classical type of time-fractional telegraph equation defined by Caputo sense for (1<α≤2). The presented method which is coupled of the radial basis functions and finite difference scheme achieves the semi-discrete solution. We investigate the stability, convergence and theoretical analysis of the scheme which verify the validity of the proposed method. Numerical results show the simplicity and accuracy of the presented method.

http://www.sciencedirect.com/science/article/pii/S0955799713002099