In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable t1−α, e(1−α)t and non-conformable t−α kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0<α≤1. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives.

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UDC 517.5 By using the definition of modified  ( h , m , s ) -convex functions of the second type, we present various refinements of the classical Hermite–Hadamard inequality obtained  within the framework of weighted integrals. Throughout the paper, we show that various known results available from the literature can be obtained as particular cases of our results.