Turkish Journal of Science
Journal license

Journal

Turkish Journal of Science


Volume
& Issue

Volume 10, Issue 3


Published
on

December 21, 2025


Pages

143-158


DOI

Article

Integral Inequalities Involving k−Atangana-Baleanu Fractional Integral Operators

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Authors

Ebru KARADUMAN Affiliation:
Department of Mathematics, Faculty of Science and Letters, Ag˘rı I˙brahim C¸ ec¸en University, 04100, Ag˘rı, Tu¨rkiye
and Aybuke BIDIL Affiliation:
Institute of Graduate Studies, Department of Mathematics, Agrı Ibrahim Cecen University, Agrı, Turkiye


Abstract

As an alternative to the classical Riemann–Liouville and Caputo definitions, newly developed fractional derivative and integral operators allow for a more accurate representation of complex processes such as memory and uncertainty. Introduced in 2017 by Atangana and Baleanu, Atangana–Baleanu frac- tional integral and derivative are distinguished by their Mittag–Leffler type kernels, which provide a non-singular structure and enable more realistic models for numerous physical and engineering problems. The advantages offered by Atangana–Baleanu fractional integral, when combined with inequality theory, yield significant contributions by offering new perspectives in theoretical mathematics and effective meth- ods for solving applied problems. In 2023, Kermausuor and Nwaeze introduced the k−Atangana–Baleanu fractional integral, a generalized version of the Atangana–Baleanu fractional integral. Based on the newly introduced k−Atangana–Baleanu fractional integral operator, novel Bullen-type inequalities involving con- vex functions have been established.


Keywords

Hermite-Hadamard inequality, Bullen inequality, Atangana-Baleanu fractional integral, k−Atangana-Baleanu fractional.


Citation

Karaduman, E. & Bidil, A. (2025). Integral inequalities involving k−atangana-baleanu fractional integral operators. Turkish Journal of Science, 10(3), 143–158. https://doi.org/10.66833/TJOS-2025-0014

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