Cangul I.N.Cevik A.S.Simsek Y.2020-03-262020-03-2620151229-3067https://dx.doi.org/10.17777/ascm.2015.25.2.211https://hdl.handle.net/20.500.12395/32819In a recent paper [16], generating functions in terms of non-negative real parameters, q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius-Euler numbers and polynomials) have been constructed by Y. Simsek. Additionally, some identities for these polynomials and numbers based on the generating functions and functional equations have been derived. Finally, a multiplication formula for the generalized Apostol type Frobenius-Euler polynomials has been given. In this paper, as a continuing study of [16], we will essentially present generalizations of the above material and, differently from aforementioned paper, we will express the interpolation functions related to these numbers and polynomials.en10.17777/ascm.2015.25.2.211info:eu-repo/semantics/closedAccessEuler numbersFrobenius-Euler numbersFrobenius-Euler polynomialsGenerating functionQ-Frobenius-Euler polynomialsQ-seriesArticle252211220N/A