  We examine the excitonic properties of layered configurations of low
dimensional transition metal dichalcogenides (LTMDCs) using the fractional
dimensional space approach. The binding energies of the exciton, trion and
biexciton in LTMDCs of varying layers are analyzed, and linked to the
dimensionality parameter $\alpha$, which provides insight into critical
electro-optical properties (relative oscillator strength, absorption spectrum,
exciton-exciton interaction) of the material systems. The usefulness of
$\alpha$ is highlighted by its independence of the physical mechanisms
underlying the confinement effects of geometrical structures. Our estimates of
the binding energies of exciton complexes for the monolayer configuration of
transition metal dichalcogenides suggest a non-collinear structure for the
trion and a positronium-molecule-like square structure for the biexciton.
