Over the last two decades, important efforts have been undertaken by the most prominent space agencies to explore and analyze the interior, ground and atmosphere of Mars. A series of remote sensing instruments have been deployed and operated to characterize the atmospheric composition and dynamics. Several techniques have been used including solar occultation spectroscopy recording the sun spectrum attenuated through the atmosphere. We present three different methods dedicated to the analysis of occultation observations in the ultraviolet (UV) wavelength range covering the Hartley band of ozone. These methods are designed to account for several absorbing gases as well as aerosols responsible for extinction along the observing line-of-sight passing through the atmosphere. The aerosols are described using a local extinction parameter at a reference wavelength and a so-called Angström α-parameter to express the wavelength dependency of extinction with a power law. In a first method, inverse Abel transform of the total extinction parameter (or optical thickness) of the atmosphere is conducted at each wavelength using a least-squares fitting technique, followed by a second least squares estimate of the local atmospheric properties at all fitting altitudes, separately. A second method is derived in which all the atmospheric gas concentrations and aerosol extinction coefficient at reference wavelength vary with altitude in a piecewise linear manner. The α parameter is however assumed to be a piecewise linear function of ln(r), allowing for numerical and analytic developments. For the sake of inversion of the observation, the gas densities and aerosol reference extinction parameters are expressed as a function of the α parameters using a linear least-squares fitting expression, so that the α parameters can be estimated using a non-linear least-squares fitting method. A third method is derived in which the gas species are approximated using piecewise exponential branches. Tests are conducted to evaluate the efficiency of all methods against retrieval of a prescribed atmospheric profile. It is found that the first two methods can readily retrieve the atmospheric properties, the second one allowing for more consistent uncertainty estimates. The third method is found to be computationally expensive with a difficult-to-reach fitting convergence. Preliminary tests are conducted using TGO-NOMAD-UVIS observations in the O3 Hartley band wavelength range. It is found that the CO2 extinction is too weak to allow retrieval of the CO2 density profile from observations at those wavelengths, while the O3 density and dust properties can be successfully retrieved.