Akademik Veri Yönetim Sistemi
Engineering Applications of Artificial Intelligence, cilt.162, 2025 (SCI-Expanded, Scopus)
This paper introduces a novel class of fractional Bullen-type inequalities, developed through the application of generalized fractional operators to functions that are twice differentiable. Diverging from conventional methodologies that typically rely on function convexity, our approach harnesses bounds on the second derivative to establish these inequalities. This key innovation allows us to derive new results without requiring convexity assumptions The flexibility of the proposed framework is illustrated by showing that, with certain parameter choices, our fractional inequalities naturally simplify to known results. So, this approach not only confirms existing findings but also expands and enhances the range of inequalities currently available in the literature. To validate the theoretical results, we also implement an Artificial Neural Network (ANN) model that accurately predicts the left, middle, and right sides of the Bullen-type inequalities. The strong agreement between ANN predictions and analytical outcomes demonstrates the practical utility of our approach. Further, this research advances the theoretical understanding of fractional inequalities while also providing valuable practical applications through detailed visualizations, thereby increasing the applicability and significance of the findings.