  The purpose of this work is to show that the Khalil and Katagampoula
conformable derivatives are equivalent to the simple change of variables $x$
$\rightarrow $ $x^{\alpha }/\alpha ,$ where $\alpha $ is the order of the
derivative operator, when applied to differential functions. Although this
means no \textquotedblleft new mathematics\textquotedblright\ is obtained by
working with these derivatives, it is a second purpose of this work to argue
that there is still significant value in exploring the mathematics and physical
applications of these derivatives. This work considers linear differential
equations, self-adjointness, Sturm-Liouville systems, and integral transforms.
A third purpose of this work is to contribute to the physical interpretation
when these derivatives are applied to physics and engineering. Quantum
mechanics serves as the primary backdrop for this development.
