Copyright © 2009 Kyung-Won Hwang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The main purpose of this paper is to present new -extensions of Apostol's type Euler polynomials using the fermionic -adic integral on . We define the --Euler
polynomials and obtain the interpolation functions and the Hurwitz type zeta functions
of these polynomials. We define -extensions of Apostol type's Euler polynomials of higher
order using the multivariate fermionic -adic integral on . We have the interpolation
functions of these --Euler polynomials. We also give -extensions of Apostol's type
Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of
these --Euler polynomials.