The Approximate Solution Of Fractional Differential Equations

There are five chapters in this paper. It introduces the difinition, property and application of the fractional differential equations. In this paper, a new quickly and powerful approximate method(Taylor's expansion method) is proposed. Using this method, we will get the approximate solution of the fractional differential equations.In the first chapter, the studing method and progress of the solution to the fractional differential equations are introduced all over the world.In the second chapter, Taylor's expansion method is studied for solving fractional differential equations, and several illustative examples are given to show the efficiency of the proposed method.In the third chapter, based on the analysis in the second chapter, Taylor's expansion method is used to solve complicated fractional differential equations, and high accurcy, efficiency of the method are shown by illustative examples.In the fourth chapter, the Taylor's expansion is proposed to two kinds of Abel integral equations (similar with fractional differential equations), and the modified Taylor's expansion is gived. Illustrative examples are given to show that the method in the present paper is simple, efficient and the modified method has high accuracy.In the fifth chapter, the above studied problems are concluded, Illustrative examples demonstrate that the present method is simple, high accuracy and efficient. Along this idea of thought, more problem of approximate solution and the theorems of the method can be considered.