| In this paper,we interested in the initial value problem of the non-linear Caputo-Fabrizio(C-F)fractional differential equations(?) where 0<α<1,T>0 are given constants,0CF Dtαy(t)is C-F fractional derivative with αorder,f:[0,T]×Rd→Rd is continuous mapping satisfying one-sided Lipschitz condition<y1-y2,f(t,y1)-f(t,y2)>≤σ‖y1-y2‖2,(?) t ∈[0,T],y1,y2 ∈ Rd,where σ 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. |
