Akademik Veri Yönetim Sistemi
Journal of Applied Analysis and Computation, cilt.16, sa.5, ss.2720-2750, 2026 (SCI-Expanded, Scopus)
In this study we explore the development of a branch of the theory of fractional integration by presenting a new methodological framework based on generalized fractional integrals, focusing on interval functions. This framework enables the more systematic and clear derivation of advanced Hermit-Hadamard inequalities suitable for convex functions. This work integrates Riemann-Liouville fractional inequalities with the classical form of Hermit-Hadamard inequalities for LR convex functions within a unified structure, eliminating the need for separate case studies or independent proofs for each inequality. This research also extends to the development of new Hermite-Hadamard inequalities targeting LR convex functions with interval values, further increasing the comprehensiveness of this proposed framework. The theoretical results obtained in this research are validated through discussions on examples and illustrations that show their application in the field of fractional integration inequalities. Artificial neural networks were also used in this research to correctly forecast the boundaries associated with inequalities in this field, increasing the reliability of this research’s results.