Lacunary interpolation by the Spline Function of Fractional Degree

Abstract

In almost all fields of numerical analysis, spline functions are the most effective tool for polynomials employed as the fundamental method of approximation theory. Additionally, existence, uniqueness, and error boundaries are required for the spline creation in the g-spline interpolation issue. Mathematics, physics, biology, engineering, signal processing, systems identification, control theory, finance, and fractional dynamics have all shown an interest in fractional differential equations, also work in social sciences including economics, finance, and dietary supplements. It is crucial to find both close and accurate solutions of fractional differential equations. To find solutions of fractional differential equations, several analytical and numerical techniques have been developed. In this paper, we extend the five-degree spline (0,4) lacunary interpolation on uniform meshes. The outcomes, uniqueness and error boundaries for generalize (0,4) Lacunary interpolation using five- degree splines. These generalizes outperform the usage of the (0,4) five splines for interpolation.