Abstract. By introducing a cartesian-like pseudocoordinate, and starting with the general Wigner commutation relations for the canonical variables of a Bose-like oscillator of a single degree of freedom, an expression for the momentum operator in a fractional dimensional space is found. The wave function that describes the motion of a free particl e is also obtained. The existence of compression (spread) of the probability density for dimensions D < 1 (D > 1) is showed. This interesting behavior suggests a strong relation between the dimensional parameter and the degree of confinement and justifies the use of fractional dimensional space approaches in modeling low-dimens ional systems.

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