A new analytical modelling for fractional telegraph equation via Elzaki transform

The main aim of this paper is to propose a new and simple algorithm for space-fractional telegraph equation, namely new fractional homotopy analysis transform method (FHATM). The fractional homotopy analysis transform method is an innovative adjustment in Elzaki transform algorithm (ETA) and makes the calculation much sim-pler. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. Finally, several numerical ex-amples are given to illustrate the accuracy and stability of this method

Numerical approximation for a variable-order nonlinear reaction-subdiffusion equation

Natural Science Foundation of Fujian province [2009J01014]Fractional reaction-subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction-subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples