Adomian Decomposition Method For Sloving Nonlinear Fractional Integral Equations

In recent years, the theory of fractional calculus is widely used in the science field, such as colored noise, fluid dynamics, chaotic phenomena, biological engineering and so on. Many practical problems can be described by the fractional calculus equations. However the linear of fractional calculus can not meet the needs of practical problems. Therefore, the improvement of the theory of fractional caclculus has become an important work. Adomian decomposition method is one of the methods for solving all kinds of linear and nonlinear equations, especially in solving nonlinear and stochastic problems, without the help of linearization and perturbation processing. Compared with the traditional numerical methods, computational process of Adomian decomposition method is relatively simple、rapid convergence、wide application. In this article will use Adomian decomposition method to solve several classes of nonlinear fractional integral equations and integral equations.This paper consists of six parts:In Chapter 1, mainly on the research background, purpose and research significance and research status at home and abroad are briefly stated.In Chapter 2, the different forms of definition and operational properties of fractional calculus, Adomian decomposition method and modification Adomian decomposition method are given.In Chapter 3, by combining Adomian polynomials with the definition of fractional order is used to solve nonlinear Volterra integral equations of fractional order with nonlinear fractional Volterra-Fredholm integral equation.In Chapter 4, the modification of Adomian decomposition method is used to solve the numerical solution of nonlinear quadratic fractional integral equation.In Chapter 5, Adomian decomposition method is used to study a class of the systems of nonlinear Volterra integral equations of fractional order.In Chapter 6, the main work done is summarized and the future outlook of the work is proposed.