Spline is a collection of mathematical functions is used to draw smooth curves through a set of points. Splines have applications in computer graphics, image processing, robotics, planning, and data interpolation. Fractional continuity is a mathematical and computer-graphics term that enhances the concept of continuity in curve and surface modeling. In this paper, the concept of fractional order continuity of generalized spline functions, an interpolating continuity class 𝐶 𝑛−1+𝛼 , 0 < 𝛼 < 1, , is presented, which gives visually piece wise smooth curves. Firstly the general algorithm for generalized polynomial splines is presented, after that it elaborate with different degree of splines. The special cases of the proposed work are also presented. The Caputo left hand and right hand fractional derivative are used in proposed algorithm. The curve produced by proposed algorithm are also control with the help of shape parameters u and v.