Fractal Inspired Models of quark and gluon distributions and longitudinal structure function FL (x, Q2) at small x

In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F _L (x, Q ²) within this approach. We make predictions using the Quantum Chromodynamics (QCD) based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible with the QCD expectation.