The aim of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities for exponentially s,m-convex functions. To establish these inequalities, we will utilize generalized fractional integral operators containing the Mittag-Leffler function in their kernels via a monotone function. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for s-convex, m-convex, s,m-convex, exponentially convex, exponentially s-convex, and convex functions.

At present, the treatment of landfill leachate is an unavoidable challenge facing environmental problems. Incineration is one of the effective methods to treat landfill leachate which meets the 3T+E principle and can avoid the production of dioxin in the process of treatment. Based on the 3T+E principle, this paper studied the influence of burner arrangement on the treatment of landfill leachate through the numerical simulation method. The research showed that the symmetrical arrangement of reverse swirl and same direction flow were more conducive to the combustion of landfill leachate concentrations in the incinerator so that the residence time of the flue gas in the second combustion chamber can also exceed 2 s. When the nozzle arrangement height is 0.9 m–0.8 m, the wall collision rate of concentrated liquid droplets can be reduced, and the burnout rate of landfill leachate was the highest, reaching more than 92%.