March, 2026

33-44

Sinan Aslan

This study introduces a novel family of refined Milne-type inequalities formulated via Rie- mann–Liouville fractional integral operators. Utilizing an appropriate integral identity for twice continu- ously differentiable functions, improved estimates are established for mappings whose second derivatives fulfill a strong s-convexity condition. Unlike existing contributions, the obtained results provide improved error estimates by incorporating the modulus parameter and exploiting the structure of strongly s-convexity more effectively. Several inequalities are established via Ho¨lder and Young integral inequalities, leading to tighter upper bounds compared to previously known results. Furthermore, special cases are discussed to demonstrate the consistency of the results with classical inequalities, including Simpson- and Newton-type estimates. The findings presented here extend and complement earlier studies in fractional inequality theory and contribute to a more precise understanding of numerical integration errors under generalized convexity assumptions.

Aslan, S. (2026) Refined Fractional Milne-Type Inequalities via Strongly s−Convexity with Enhanced Error Bounds. Turkish Journal of Science. 11(1) 33-44.