Analysis Of Nurmericaltreatment For Fractionaldifferntialequations

Fractional differential equation is the promotion of classical integer-order differential equations,It replaces the derivative of integer order with fractional derivative, fractional differential equations in different fields of science has been widely used. Therefore, it has also attracted widespread research attention. Fractional differential equations compares with integer order calculus, the most important advantage is that it can better simulate the dynamic nature of the physical processes and system processes.The main research is fractional derivative of Caputo fractional derivatives and Riemann-Liouville fractional derivatives. They are almost the same to promote the classical derivative. Riemann-Liouville is more perfect than Caputo fractional derivatives in mathematic, but it needs more demanding requirements of the initial value, when fractional differential equations or physical interpretation not clear, the initial value is difficult to give. Caputo fractional derivative of the initial request is simple.In this paper we study the fractional derivative given by Caputo, Discussed fractional order differential equations depending on the parameters and numerical approach.The first chapter we review the production of fractional differential equations and the development of recent decades, introduced fractional differential equations in different fields of application by introducing some specific examples. Discussed the fractional differential operator of the definition and development, compared some links and differences.In chapter two, we first introduce the existence and uniqueness condition of fractional differential equations. Under the existence and uniqueness conditions, we discussed fractional differential equations dependence on the fractional derivative, the initial value conditions and differential equation right hand side.In chapter three, we present a predictor-corrector method for our model of fractional differential equations, we detailed the construction of the prediction process of correction, discussed the prediction error correction sector. Finally, We adopted the numerical results of a numerical example to prove that theoretical analysis in good agreement nature, and the feasibility of calculation.