The Solution To Several Classes Of Differential Equations

Fractional differential equations have becoming a hot research point of fractional calculus theory. With the appearance of fractional differential equations in more and more science fields, the solution of these equations is becoming particularly urgent. However, the vast majority of fractional order differential equations can’t calculate the accurate analytic solution, it must use the approximate method to obtain the approxi-mate analytical solution and even the exact exact solution, in this way it can facilitate the theoretical analysis and practical calculation and more preponderance than simple numerical solution.In the present paper the approximate analytical solution of several types of the fractional order differential equations is deduced with the help of powerful operator method, homotopy analysis method, homotopy perturbation method and DGJ method, respectively.This paper consists of four chapters:In chapter 1, we mainly introduce domestic and foreign research status about the approximate analytical solution of the fractional order differential equations, and provide some background knowledge and preliminaries.In chapter 2, the operator method is used to obtain the approximate analytical solution of a class of fractional differential equations with Laguerre derivative.In chapter 3, the basic principle of homotopy analysis method is comprehensively introduced, and its successful applied to solving a boundary value problem on a class of fractional differential equations with Laguerre derivative: and the time-fractional diffusion equation initial value problem:In chapter 4, we study the following initial value problem on a class of nonlinear fractional equations:We use the homotopy perturbation method and DGJ method to solve the nonlinear time-fractional hyperbolic equation: the nonlinear time-fractional advection partial differential equation: and the nonlinear time-fractional Fisher’s equation:...