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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].

Relations on the Apostol Type (p, q)-Frobenius-Euler Polynomials and Generalizations of the Srivastava-Pintér Addition Theorems