The Adomian Decomposition Method For The Mon-Linear Anomalous Subdiffusion Equation And The Fractional Rayleigh-Stokes Problem

In recent years, fractional calculation plays a more and more important role in various fields of science, especially in engineering, physics, finance, and hydrology. Differential equations with fractional order have recently proved to be valuable tools to modeling of many physical phenomena. Recently, the nonlinear anomalous subdiffusion equation(NA-SubDE) and the Rayleigh-Stokes problem for a heated generalized second grade fluid(RSp-hgsgf) have been treated by many authors. However, effective methods for the non-linear anomalous subdiffusion equation (NA-SubE) are still in their infancy. Furthermore, the reality value of exact solutions of the velocity and temperature fields of RSp-hgsgf are difficult to compute.In this paper, we discuss the non-linear anomalous subdiffusion equation and the Rayleigh-Stokes problem for a heated generalized second grade fluid by using Adomian decomposition method. The Adomian decomposition method can perfectly deal with nonlinear term, and provide highly accurate numerical solution without discretization for the problem. The overall errors can be reduced to a much smaller extent by adding new terms of the decomposition series. We can obtain approximate solution of the non-linear anomalous subdiffusion equation by using Adomian decomposition method. For the Rayleigh-Stokes problem for a heated generalized second grade fluid(RSp-hgsgf), we can obtain approximate solutions of the velocity and temperature fields of RSp-hgsgf by using Adomian decomposition method. Numerical examples are presented in each chapter, which verify the efficiency of the above numerical method. The techniques can also be applied to deal with other types of fractional order differential equations.