We study polarons confined in parabolic quantum wells and parabolic quantum well wires within the framework of the fractional-dimensional space approach. In this scheme, the real confined `polaron plus parabolic confining potential' system is mapped into an effective fractional-dimensional bulk in which the polaron behaves in an unconfined way, and the fractional dimension is essentially related to the degree of confinement of the actual system. We find analytical expressions which allow a very simple estimation of the corresponding polaron corrections. The fractional-dimensional theoretical results are shown to be in overall agreement with previous, more detailed, calculations.