Newton-type inequalities for the class of modified hyperbolic p-convex functions via Riemann-Liouville fractional integrals with numerical justifications

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.