Integral inequalities involving k-Atangana-Baleanu fractional integral operators

In recent years, fractional analysis has attracted significant attention in both pure mathematics and applied sciences, emerging as a powerful tool in the modeling of differential equations. 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 2016 by Atangana and Baleanu, the Atangana–Baleanu fractional integral and derivative are distinguished by their Mittag–Leffler type kernels, which provide a nonsingular structure and enable more realistic models for numerous physical and engineering problems. The advantages offered by the Atangana–Baleanu fractional integral, when combined with inequality theory, yield significant contributions by offering new perspectives in theoretical mathematics and effective methods for solving applied problems. In 2023, Kermausuor and Nwaeze introduced a generalized version of the Atangana–Baleanu fractional integral. In this thesis, based on the newly introduced Atangana–Baleanu fractional integral operator, Bullen-type inequalities involving convex functions have been established.