In the present paper, we introduce Eulerian polynomials with parameters $a$ and $b$ and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give relations between Eulerian polynomials with parameters $a$ and $b$, Bernstein polynomials, Poly-logarithm functions, Bernoulli and Euler numbers. Moreover, we see that our polynomials at $a = -1$ are related to Euler-Zeta function at negative integers. Finally, we get Witt's formula for new generalization of Eulerian polynomials which we express in this paper.