eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2017-06-14 5 4 126 131 10.12691/tjant-5-4-2 TJANT2017542 article Burak Kurt burakkurt@akdeniz.edu.tr 1 Department of Mathematics, Faculty of Educations, University of Akdeniz In this work, we define and introduce a new kind of the Apostol type Frobenius-Euler polynomials based on the (p, q)-calculus and investigate their some properties, recurrence relationships and so on. We give some identities at this polynomial. Moreover, we get (p, q)-extension of Carlitz's main result in [1]. http://pubs.sciepub.com/tjant/5/4/2/tjant-5-4-2.pdf Generating function Frobenius-Euler polynomials and numbers (p, q)-calculus (p, q)-Frobenius-Euler polynomials Apostol-Bernoulli number and polynomials generalized q-Bernoulli polynomials generalized q-Euler polynomials