Research On The Solution Of Fractional Differential Equations

It is important to study the fractional calculus operator in the field of nonlinear. But the nonlinear fractional differential equation is difficult to solve, based on the analysis of current research, papers research on existence and uniqueness of solutions for initial value problems of R-L fractional differential equations and its analytical method.The existence and uniqueness of solutions for initial value problems of R-L fractional differential equations are investigated, giving the fractional equation Peano existence theorem and inequality theorem, based on the successive approximation approach, using Tonelli sequence and Ascoli lemma to prove that the Peano existence theorem of R-L fractional differential equation. According to the fractional inequalities proved the uniqueness of R-L fractional differential equations.An improved generalized differential transform method is proposed for solving the approximate analytical solution of nonlinear fractional differential equation in the definition of R-L. The method which is a combination with differential transform method,Adomian polynomial, Padé approximation. The method has little calculation and higher accuracy. Finally, numerical example is given to verify the effectiveness of the algorithm.Using the Wavelet-Galerkin method to solve the fractional equations and the effectiveness of the algorithm is verified by numerical examples. The results show that the method has stronger stability and ideal precision, it is suitable for solving fractional equation.Combined with Adomian method and the perturbation method to solve fractional equations.In order to make the number of series solution of equation fewer and get precision much higher. The effectiveness of the algorithm is verified by a numerical example.