Using Generalized Differential Transform Method And Wavelet To Solve Three Class Of The Fractional Integral And Differential Equations

Wavelet analysis method is a new way to solve fractional differential equations inrecent years. Therefore, it is better than the traditional Fourier analysis with a moredetailed video analysis capability to better deal with the problem of local existence ofsingularities. Fractional differential equations have been study by differential transformmethod. Nonlinear fractional differential equation and its solution of the nonlinear scienceresearch as a cutting-edge research topics and hot issues, with great challenge.The paper firstly introduces the development history of wavelet analysis, nonlinearfractional integral-differential equations and some work about fractional differentialequations at present. Then we give the definitions and the properties of wavelets andgeneralized differential transform method, some prior knowledge of fractional differentialequations and the wavelets.Secondly, the paper mainly research methods of solving the Volterra equation byusing the generalized differential transform method. The nonlinear fractionalintegral-differential equations which are both transformed into nonlinear algebraicequations. The numerical example shows that the method is effective and accurate.Finally, The second Chebyshev wavelets is adopted to solve the nonlinear fractionalintegral-differential equations which are both transformed into nonlinear algebraicequations by using differential operator matrix and the product operation matrix. At thesame time given error analysis, the numerical examples verify the validity of the proposedmethod. The Chebyshev wavelets are adopted to solve the fractional integral-differentialequation of Bratu-type. At the same time given the proof of uniqueness and convergence,according the error analysis we receive the maximum absolute error, under the conditionof no exact solutions, using error estimation type we can also be very good to estimateerror. Give the numerical examples verify the validity of the proposed method.