Numerical Solution And Analytic Solution For Two Classes Fractional Differential Equation

Fractional differential equations can simulate scientific many phenomena in engineering, Physics and biology. Therefore, more and more scholars research in fractional differential equations.In this paper, numerical solutions and analytic solutions for two classes fractional differential Equation are researched. The first class is fractional telegraph equation,it is obtained from classical telegraph equation by replacing the first-order time derivative,the second-order time derivative with fractional derivatives.For fractional telegraph equation,we discuss its analytic solution using Adomian method and set an example to compare the analytic solution with exact solution,which can show the method is effective.Secondly, its numerical solution is discussed. We construct the implicit difference scheme and prove the stability and convergence of the implicit difference scheme. Lastly,we set an numerical example which shows the method is effective. The second class is to extend the space-time fractional convection and diffusion equation,namely the generalized space-time fractional convection and diffusion equation is obtained from the space-time fractional convection and diffusion equation by replacing the first-order space derivative.Its numerical solution is discussed, the implicit difference scheme is constructed and the stability and convergence of the implicit difference scheme is proved. An numerical example is set to compare the numerical solution and example solution,which shows the method is effective. Its analytic solution is disscused using vatiational iteration method. An numerical example is set ,and it shows that the method is effective. Key Words:...