Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D-q and divided difference. As applications of the post-quantum calculus ...

In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral ...

In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: D-q(gamma)(phi(p)(D(q)(delta)y(t))) + f(t,y(t)) = 0 ...

In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of ...

The Newton power-sum formulas relate to sums of powers of roots of a polynomial with the coefficients of the polynomial. In this paper we obtain formulas that relate to sums of reciprocal powers of zeros and poles of entire ...

In this paper, we present a further investigation for the Apostol-Bernoulh polynomials and the Apostol-Genocchi polynomials. By making use of the generating function methods and summation transform techniques, we establish ...

The significance of multi-variable special polynomials has been identified both in mathematical and applied frameworks. The article aims to focus on a new class of 3-variable Legendre-truncated-exponential-based Sheffer ...