A generalization of the Apostol-type Frobenius–Genocchi polynomials of level 1

The main objective of this paper is to present the generalized Apostol-type Frobenius–Genocchi polynomials and numbers of level ι and order α. We give some basic identities and properties (summation formula, differential and integral relations, addition theorems, and so on) via generating function techniques. Also, we provide certain relationships between these polynomials and the Stirling numbers of the second kind and other polynomial families. Finally, we obtain a differential equation and a recurrence relation for these polynomials.