Generalized Quartic Fractional Spline Interpolation with Applications

Abstract

In this paper, a new fractional spline function of polynomial form with the idea of the lacunary interpolation is considered to find approximate solution for fractional differential equations (FDEs). The proposed method is applicable for α ∈ (0, 1], where α denotes the order of the fractional derivative in the Caputo sense. Convergence analysis of the method is considered. Some illustrative examples are presented and the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems. The study is conducted through illustrative examples and error analysis. keywords: Fractional integral and derivative, Caputo Derivative, Taylor’s expansion, Error bound, Spline functions. 68 Faraidun K. Hamasalh and Pshtiwan O. Muhammad