Algorithm Research Of Fokker-planck Equation With Caputo-fabrizio Fractional Derivative

Fractional calculus appeared as the promotion of integer derivative.On the one hand,its equations promoted the development of fractional calculus theory to some extent,on the other hand,it attracted the attention of scholars and was widely used in various fields.Such as ocean dynamics,fluid dynamics,superconductivity and economic and financial fields.However,fractional calculus equations can accurately explain some nonlinear problems in mathematical physics,the analytical solution of Fractional calculus equation is difficult to get in general.Therefore,it is very important to obtain the theoretical significance and application value of numerical solutions.This article explores two numerical solutions of Fokker-Planck equation which contains fractional derivative with Caputo-Fabrizio.First of all,the Ritz approxima-tion is considered to solve linear of the Fokker-Planck equation with the fractional derivative of Caputo-Fabrizio.Secondly,We can turn the Fokker Planck equation into an optimization problem and use polynomial function to obtain the algebraic e-quations.Finally,we can solve the nonlinear algebraic equations.We also discussed the convergence of this method and illustrate the effectiveness and applicability of the method by numerical examples.Moreover,basing on the regenerative nuclear theory,there is a solving method including umerically solving the Fokker-Planck equation of the fractional derivative of Caputo-Fabrizio constructing two-dimensional regenerative nuclear space and turning this problem to solving nonlinear equations.This method avoids the use of the process of gram-schmidt orthogonalization and improves the speed of calcu-lation.Finally,a numerical example is given to illustrate the effectiveness of the method.