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February 9, 2026Open Access

Some novel fractional Milne-type inequalities for twice differentiable s-convex functions in the second sense

Key Points

The aim is to derive novel fractional Milne-type inequalities for twice differentiable s-convex functions.
Utilization of a special identity for twice differentiable functions.
Application of Riemann-Liouville fractional integrals.
Use of H?lder and Young inequalities to prove results.
New fractional Milne-type inequalities are established for s-convex functions.
Results provide fresh insights into the analysis of s-convex functions.
The identity used enhances understanding of the behavior of second derivatives in these functions.

Abstract

In this paper, a special identity for twice differentiable functions, which is available in the literature, is utilized. By combining this identity with Riemann-Liouville fractional integrals, various fractional Milne-type inequalities are obtained for functions whose second derivatives in absolute value are s-convex in the second sense. Moreover, H?lder and Young inequalities are used to prove the different and original results. These approaches contribute to the analysis of s-convex functions and offer new perspectives in the field of fractional analysis.

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