Investigation of Fractional Spline Function-Based Lacunary Interpolation with Convergence Analysis

Abstract

This paper presents a derived fractional degree (1/2, 3/2, 5/2) lacunary interpolation technique. We demonstrate the proper representation of complex functions and their evolution throughout the specified interval utilizing the three-spline function. The advanced modified extended spline technique is employed to achieve many types of boundary conditions, including fractional order brightness. The impact of the fractional derivative on the model is illustrated through convergence analysis simulated for different values of beta. Issues related to spline functions can be addressed using this interpolation method for the construction of spline functions.