We study linear q-difference-differential equations under the action of a perturbation parameter . This work deals with a q-analog of the research made in (Lastra and Malek in Adv. Differ. Equ. 2015:200, 2015) giving rise to a generalization of the work (Malek in Funkc. Ekvacioj, 2015, to appear). This generalization is related to the nature of the forcing term which suggests the use of a q-analog of an acceleration procedure. The proof leans on a q-analog of the so-called Ramis-Sibuya theorem which entails two distinct q-Gevrey orders. The work concludes with an application of the main result when the forcing term solves a related problem
