θ Method For Fractional Differential Equation

With the development of science and technology,the fractional derivatives play an increasingly important role in many scientific fields,especially in viscoelastic materials,hydrology geography,fractal kinetics,diffusion and transportation and bioengineering,etc.The two classes of model equation considered in the paper are commonly discussed in the study of fractional differential equation.The time fractional partial differential equation can be transformed into this two classes of model equation by discretion in space.Therefore,the two classes of equation discussed are typical,which has a good prospect of application.The structure of this paper is as follows:In chapter 2,a fractionalθMethod is proposed for fractional differential equationⅠ.Then,we performed consistency analysis,convergence analysis and stability analysis.Finally,numerical experiments are provided for the valid of the methods.In chapter 3,a fractionalθMethod for fractional differential equationⅡis considered,we give the consistency analysis and apply this method to the equation in computational biology.The numerical experiments show that fractionalθmethod is simple and valid.