Adomian Decomposition Method Of Fractional Differential Equations

In recent years, Fractional differential equations have been widely used in various fields, such as Physics, Mechanics, Biology, and Medicine etc. and great success has been gained already. From the general review of its development, it not only shows profound research background and good application fundamentals, but also has a wide development space. Therefore, it seems very important to study the basic theory, nature and solution of fractional differential equations. These researches establish a solid foundation for further application of fractional differential equations.This Paper has done works as follows:First, we expound two important and basic definitions of fractional calculus theory: Riemann-Liouville fractional calculus and Caputo fractional derivatives; discuss the relationship between them and basic operation nature. We consider a class of fractional linear differential equations, and investigate the existence and uniqueness of solutions for fractional differential equations by using integral transform. Second, we prove the convergence of the fractional linear differential equations based on the Caputo fractional derivative by using Adomian decomposition method. We use this method solve the Bagley-Torvik equationand half space fractional differential equations for the boundary problemThird, the fractional nonlinear convection-diffusion equation with external force and absorption in finite fractal media is given as follows:Consider the above equation with the initial conditionc(x,0)=(?)(x)we derive a solution in the form of a series by using Adomian decomposition method.