We present the results for a chemical abundance analysis between planet-hosting and stars without planets for 12 refractory elements for a total of 1111 nearby FGK dwarf stars observed within the context of the HARPS GTO programs. Of these stars, 109 are known to harbour high-mass planetary companions and 26 stars are hosting exclusively Neptunians and super-Earths. We found that the [X/Fe] ratios for Mg, Al, Si, Sc, and Ti both for giant and low-mass planet hosts are systematically higher than those of comparison stars at low metallicities ([Fe/H] ≲ from -0.2 to 0.1 dex depending on the element). The most evident discrepancy between planet-hosting and stars without planets is observed for Mg. Our data suggest that the planet incidence is greater among the thick disk population than among the thin disk for mettallicities bellow -0.3 dex. After examining the [α/Fe] trends of the planet host and non-host samples we conclude that a certain chemical composition, and not the Galactic birth place of the stars, is the determinating factor for that. The inspection of the Galactic orbital parameters and kinematics of the planet-hosting stars shows that Neptunian hosts tend to belong to the "thicker" disk compared to their high-mass planet-hosting counterparts. We also found that Neptunian hosts follow the distribution of high-α stars in the UW vs. V velocities space, but they are more enhanced in Mg than high-α stars without planetary companions. Our results indicate that some metals other than iron may also have an important contribution to planet formation if the amount of iron is low. These results may provide strong constraints for the models of planet formation, especially for planets with low mass. Based on observations collected at the La Silla Parana Observatory, ESO (Chile) with the HARPS spectrograph at the 3.6-m telescope (ESO runs ID 72.C-0488, 082.C-0212, and 085.C-0063).