One fractional spline interpolation is presented in this paper for the solution fractional initial value problems that is with spline interpolation as a new class depended on class splines as a method to approximate the exact solution of such problem. Error bounds were discussed as the presented spline function. On other hands, stability analysis has been accomplished and two examples were chosen as consideration for the numerical explanation of the presented technique. The outcome demonstrates that the presented fractional cubic spline function which interpolates the lacunary data acted as an efficient and effective way to solve such kind Special problems.