Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
Advances in Fractional Milne-Type Inequalities for Convexity and Their Applications
Bibi, N., Saleem, M., Munir, A., Qayyum, A., Ghareeb, S., Muawwaz, M.
Corresponding Email: muawwaz123@gmail.com
Received date: 17 September 2025
Accepted date: 16 November 2025
Abstract:
Fractional calculus serves as a fundamental framework in mathematics, applied sciences, and the study of integral inequalities, offering versatile tools for modeling complex phenomena. This study focuses on establishing new Milne-type inequalities for various classes of functions within the framework of Atangana-Baleanu fractional integrals. The main contributions include fractional Milne-type inequalities for bounded functions, derived as special cases of the presented theorems and supported by illustrative examples. Furthermore, the work presents applications to the q-digamma function and provides refined error estimates associated with the generalized Milne-type quadrature formula.
Keywords: Convex functions; Atangana-Baleanu fractional integrals; bounded function; q-digamma functions; Young's inequality.
