Stability And Convergence Of A Class Of Difference Method For Nonlinear Fractional Differential Equations With Caputo-Fabrizio Derivative

In this paper,we interested in the initial value problem of the non-linear Caputo-Fabrizio(C-F)fractional differential equations(?) where 0<?<1,T>0 are given constants,0CF Dt?y(t)is C-F fractional derivative with ?order,f:[0,T]×Rd?Rd is continuous mapping satisfying one-sided Lipschitz condition<y1-y2,f(t,y1)-f(t,y2)>???y1-y2?2,(?) t ?[0,T],y1,y2 ? Rd,where ? is real constant.We obtained an available numerical method,by using the interpolation derivative formula approximate the first derivative,which can be used to solve the fractional differential equation with C-F derivative.The stability and convergence of the method are discussed.Numerical examples are given to illustrate the difference method efficiency and the theoretical analysis validity.