Fractional Order Reproducing Kernel Method For Solving Fractional Order Differential Equation With Caputo-Fabrizio Derivatives

This paper mainly discusses the fractional reproduing kernel method in the sense of Caputo-Fabrizio fractional order derivatives,and solves a differential equations with Caputo-Fabrizio fractional derivatives.Firstly,the reproduce kernel method and the Caputo-Fabrizio fractional derivative are introduced in detail,and some development property of the fractional derivative is described,but there are few studies on the Caputo-Fabrizio fractional derivative.A new fractional reproducing kernel space under the definition of this fractional derivative is constructed,the corresponding reproducing kernel function is found,and the differential equation studied is numerically approximated by using the kernel function as the basis of the space.The error estimation of the algorithm is carried out through the effective derivation process,and the convergence and stability analysis are given.Finally,the corresponding numerical examples are given,and the numerical results of this method are compared with those of other literature,and the results show that the proposed method has high accuracy and effectiveness.