In this paper, new generalizations of Newton-type inequalities for the class of strongly convex functions by utilizing Riemann–Liouville fractional integrals are established. New estimates are obtained for functions that are strongly convex. The established inequalities are further improved. Examples, along with graphs, are provided to demonstrate the validity of the newly established inequalities and comparisons with existing results. It is expected that the results of this paper will open up new avenues of research and may be generalized to other types of fractional operators and generalized convex functions.

In this paper, an identity involving Riemann-Liouville fractional integrals is established which serves as the basis for several new Newton-type inequalities involving the modified class of hyperbolic p -convex property of differentiable functions. Some new inequalities are also derived for functions of bounded variation. Examples along with graphs are provided to demonstrate the validity of the newly established inequalities, and the comparison with earlier results highlights their enhanced applicability and significance.

In this article, new estimations of the integral form of the midpoint formula are derived for p ‐convex functions via Katugampola fractional integrals. A specific identity for differentiable functions is established, which extends and strengthens the integral midpoint inequality through innovative estimations. Moreover, estimations of the integral form of the midpoint formula are developed for functions whose first derivatives in absolute value are p ‐convex, employing Katugampola fractional integrals. Examples with graphs are presented to validate the results, and a comparison with previous findings demonstrates the superiority of the newly obtained inequalities.

In this paper, Riemann–Liouville fractional integrals are employed to prove several new Newton‐type inequalities related to the modified class of p ‐convex property of differentiable functions. Some more inequalities are also derived for functions of bounded variation. Examples along with bar charts, contour plots, 2D, and 3D graphs are provided to demonstrate the validity of the newly established inequalities, along with the numerical simulations of comparisons with earlier results.