Weddle's inequalities in fractional space

The literature clearly demonstrates the investigation of various approaches, including Newton–Cotes procedures, to approximate the integrals with high accuracy. A closed method based on seven points that approximates the quantities by a sixth-degree polynomial is known as Weddle's rule. This study assesses the error analysis of this renowned procedure to seek out the shortcomings of classic error inequality to produce new bounds for a larger space of functions within the fractional calculus. A new Riemann-Liouville fractional identity for differentiable functions is developed. To construct various estimates of Weddle's inequality, we utilize this identity together with properties of several benchmark functions like convex, Lipschitz, and bounded variation functions. Graphical and numerical comparisons are supplied to justify the obtained results. Lastly, we present the applicable analysis of primary findings to the theory of means, composite error bounds, and particularly a bi-quadratic iterative method is developed.