We pose a conjecture about Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special metrics.

In this study, some inequalities of Hermite-Hadamard type for integrals arising in conformable fractional calculus are presented. fact, the obtained not only valid those calculus, but more general as well. Numerous known versions recovered special cases. We also illustrate our findings via applications to modified Bessel functions, means, and midpoint approximations.