The fractional Cubic Spline Interpolation without using the derivative values

The paper introduces a function value based fraction of cubic spline interpolation, which is used for studying the curves and surfaces. The interpolation function has a simple and explicit mathematical representation, convenient both in practical application and in theoretical studies. It should be mentioned that the interpolating surfaces are C 1 in the interpolating region under the condition that the interpolation is only based on the function values. Moreover, properties and views are shown in matrix notation, and then the error is calculated.