What do we mean by "the luminosity fraction" and "the fractional contribution of the secondary star" of binary stars? can anyone suggest any method to calculate them theoretically?
It just means that in a star that is an unresolved binary system (i.e. the light you receive comes from both stars), the secondary contributes a fraction of that light.
This fraction could be expressed as a fraction of the total luminosity or a fraction of the flux at a particular wavelength or in a particular waveband.
How do you work it out theoretically? Well you would have to know exactly what kind of stars the primary and secondary were. e.g. If you knew they were both main sequence stars and you knew their masses, you could use a main sequence mass-luminosity relation to turn a mass ratio into a luminosity ratio. If you knew their temperatures, you could model their spectra to estimate the primary Vs secondary contribution at any wavelength.