Akademik Veri Yönetim Sistemi
II. International Conference on Artificial Intelligence: From Theory to Practice, Nakhchivan, Azerbaycan, 26 - 27 Mayıs 2025, ss.1304-1314, (Tam Metin Bildiri)
The Hermite-Hadamard inequality plays a fundamental role in the analysis of convex functions and integral inequalities. In this study, the classical Hermite-Hadamard inequality is extended within the framework of variable-order Riemann-Liouville fractional integral operators and s-convex functions. The new inequalities derived provide more precise upper and lower bounds compared to previous results. A new lemma involving differentiable functions for variable-order fractional integrals is first derived, and then, using this lemma, extended versions of the Hermite-Hadamard, trapezoidal, and midpoint inequalities are obtained. Furthermore, numerical examples and graphical analyses are presented to demonstrate the validity of the theoretical findings. These examples help to visualize the improvement of the proposed inequalities over the existing ones and show their practical applicability. The graphical representations further support the idea that variable-order fractional integrals offer greater flexibility and accuracy in modeling convexity-based inequalities. This work strengthens the connection between variable-order fractional analysis and convexity theory, offering new perspectives through theoretical developments and applications in optimization, engineering, and mathematical modeling. In particular, the generalized inequalities may find usage in diverse areas such as control theory, physics, economics, and signal processing, where fractional models are increasingly being employed.
By exploring the behavior of s-convex functions under fractional operators with non constant orders, this study opens up new directions for research. Future studies can explore similar inequalities for other generalized convexity concepts or develop numerical methods for approximating these integrals in practical problems.
Key words:Hermite–Hadamard inequality, Variable-Order fractional integrals, S-convex function, special functions.