On Error Approximations of Fractal Lobatto–Legendre Quadrature Rule

The Yang local fractional calculus was developed to analyze discontinuous mappings. The results obtained within this framework are equally useful in the classical sense. The study of integrals and their approximation rules is an interesting field of research. Among them, the Gaussian quadrature rules are more useful due to their accuracy. In this manuscript, we will explore the error inequalities of the four-point Lobatto–Legendre Quadrature rule incorporating fractal calculus. Our approach is based on the generation of inequalities through a generalized fractal identity. First, we develop an auxiliary result. Then, the applications of various classes of mappings are defined over Rt and auxiliary results, and we develop several new estimates. Additionally, an Artificial Neural Network (ANN) framework is used to analyse the profile and computational stability of the derived inequalities. Lastly, we have focused on the applicable analysis of the proposed results. This is the first study carried out on Lobatto-type inequalities within fractal space.