  A new kind of deformed calculus (the D-deformed calculus) that takes place in
fractional-dimensional spaces is presented. The D-deformed calculus is shown to
be an appropriate tool for treating fractional-dimensional systems in a simple
way and quite analogous to their corresponding one-dimensional partners. Two
simple systems, the free particle and the harmonic oscillator in fractional-
dimensional spaces are reconsidered into the framework of the D-deformed
quantum mechanics. Confined states in a D-deformed quantum well are studied.
D-deformed coherent states are also found.
