Chebyshev Operation Matrix:Numerical Method For Solving Fractional Differential Equation

In recent years, fractional differential equations including fractional differential equations and fractional partial differential equations have been being more and more researched. In many areas of science can be successfully modeled by the use of fractional differential equations. With the status of fractional differential equations in the application is more and more important, how to obtain the solution has become the hot spot of research.The main works is as follows:1. The first part of paper deals with the numerical solution of a class of fractional differential equations. The fractional derivatives are described in the Caputo sense. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.2. A new Chebyshev wavelet operational matrix of fractional order integration is derived by combining the definition of fractional integral with the idea of operational matrix. The Chebyshev wavelet operational matrix of the fractional order differentiation is obtained. We obtain the coefficient matrix of the function by collocation method. We have discussed the numerical method of a class of fractional partial differential equations by using the obtained operational matrix and Sylvester equation. Illustrative examples are included to demonstrate the applicability of this method.