Numerical Solution For A Class Of Fractional Differential Equation And Realization On The MATLAB

In recent years, the fractional differential equations appear more and more frequently in research areas and engineering applications. An easy-to-use and effective method for solving such equations is needed. Though some analytic solutions of fractional differential equations can be resolved,many solutions of them are expressed by some special functions. Generally, most fractional differential equations can not be resolved analytically. Hence there has been a growing interest to develop numerical techniques.We give some numerical methods to find the solution of the linear multi-term fractional differential equation And we calculate the numerical solutions using the mathematical soft Matlab, the structure of this thesis is illustrated as the following:In chapter 1, the development history and recent applications of fractional calculus are introduced concisely;The definitions and main properties of fractional derivative are given. A brief introduction of our research equation is given at the end; and the main work of the paper is summed up.In chapter 2, we firstly using the properties of the Caputo fractional derivative and using the lemma Based on the Adomian decomposition method, we develop a new numerical technique for solving linear multi-term fractional differential equation. We apply this new method to the Bagley-Torvik equation. Numerical results show that the numerical method is efficient.In chapter 3, by using the method of reduction, we reform the linear multi-term fractional differential equation to a system of fractional differential equationsTo discretize the fractional derivative we use K.Diethelm's method:We give a new numerical method to solve the fractional differential equation. We present some examples to show the efficiency and simplicity of the method.In chapter 4, we apply the Adomian decomposition method to the system of fractional differential equations Then we convert it to a equivalent form Using Adomian decomposition method, we develop a new Adomian decomposition method based on reduction. We apply it to the Bagley-Torvik equation. Numerical results and computer graphics show that the numerical method is efficient.Finally we point out the problems which will be solved in the field and the plan we will do in the future.