Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel

[摘要] At first, we construct a connection between the Atangana–Baleanu and the Riemann–Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this relationship and the iterated form of Prabhakar fractional model, we are able to find some new Hermite–Hadamard inequalities and related results on integral inequalities for the two models of fractional calculus which are defined using monotone functions with nonsingular kernels.

[学科分类] 航空航天科学

[关键词] Riemann–Liouville fractional integral;Mittag-Leffler function;Integral inequalities