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.

In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals.

In this note we obtain sufficient conditions under which we can guarantee the stability of solutions of a fractional differential equations of non conformable type and we obtain some fractional analogous theorems of the direct Lyapunov method for a given class of equations of motion.

In this paper, we present two qualitative results concerning the solutions of nonlinear generalized differential equations, with a local derivative defined by the authors in previous works. The first result covers the boundedness of solutions while the second one discusses when all the solutions are in L$^{2}$.

No abstract