In this paper we construct a new type of twisted q-Genocchi numbers and polynomials with weak weight α. We investigate some properties which are related to twisted q-Genocchi numbers G (α) n,q,w and polynomials G (α) n,q,w (x) with weak weight α. Keywords: Genocchi numbers and polynomials, twisted q-Genocchi numbers and polynomials, twisted q-Genocchi numbers and polynomials with weak weight α

Recently, Kim’s work in press introduced q-Bernstein polynomials which are different Phillips’ q-Bernstein polynomials introduced in the work by Phillips, 1996; 1997 . The purpose of this paper is to study some properties of several type Kim’s q-Bernstein polynomials to express the p-adic q-integral of these polynomials on Zp associated with Carlitz’s q-Bernoulli numbers and polynomials. Finall...

We describe the qFunctions Mathematica package for q-series and partition theory applications. This includes both experimental symbolic tools. The set of elements guessers q-difference equations recurrences given fitting/finding explicit expressions sequences polynomials. can symbolically handle formal manipulations on q-differential, recurrences, such as switching between these forms, finding ...

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...

‎in this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of malmquist type‎ $$‎sum^n_{j=1}f(z+c_j)=frac{p(f(z))}{q(f(z))}‎,$$ ‎where $n(in{mathbb{n}})geq{2}$‎, ‎and $p(f(z))$ and $q(f(z))$ are‎ ‎relatively prime polynomials in $f(z)$ with small functions as‎ ‎coefficients‎, ‎admitting a meromorphic function of finite order‎. ‎moreover‎, ‎the properties of finite o...

Later various generalizations of these operators were discovered. It has been proved as a powerful tool for numerical analysis, computer aided geometric design and solutions of differential equations. In last two decades, the applications of q-calculus has played an important role in the area of approximation theory, number theory and theoretical physics. In , Lupaş [] and in , Phillip...

Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider two new q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci polynomials and the recent works on the combinatorics of the Matrix Ansatz of the PASEP.

The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral ...