Newton’s law of cooling with generalized conformable derivatives

Abstract

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 t 1−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.