150 citations · 305 across the 41 of their papers we have counts for
45 papers
Gauss-Appell polynomials: An umbral calculus approach
Subuhi Khan, Ujair Ahmad, Mehnaz Haneef +1
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeav…
A new family of q-Bernstein polynomials: Probabilistic viewpoint
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfyin…
Certain results for unified Apostol type-truncated exponential-Gould-Hopper polynomials and their relatives
Serkan Araci, Mumtaz Riyasat, Tabinda Nahid +1
The present article aims to introduce a unified family of the Apostol type-truncated exponential-Gould-Hopper polynomials and to characterize its properties via generating function…
The Evaluation of the Sums of More General Series by Bernstein Polynomials
Mehmet Acikgoz, Ilknur Koca, Serkan Araci
Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th power of positive integers up to n. By means of that we consider the evaluation of the sum of more genera…
The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials
Serkan Araci, Mehmet Acikgoz, Armen Bagdasaryan +1
In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional wi…
Some New Symmetric Identities for the q-Zeta Type Functions
Serkan Araci, Armen Bagdasaryan, Cenap Ozel +1
The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities f…
Extended fermionic -adic integrals on
Feng Qi, Serkan Araci, Mehmet Acikgoz
In the paper, using the extended fermionic -adic integral on , the authors find some applications of the umbral calculus. From these applications, the authors deri…
Identities involving the -Genocchi polynomials and -Zeta-type function
Armen Bagdasaryan, Erdogan Sen, Yuan He +2
The fundamental objective of this paper is to obtain some interesting properties for -Genocchi numbers and polynomials by using the fermionic -adic -integra…
On the modified q-Genocchi numbers and polynomials and their applications
Serkan Araci, Armen Bagdasaryan, Erkan Agyuz +1
The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explici…
Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis
Armen Bagdasaryan, Serkan Araci, Mehmet Acikgoz +1
In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis.…
On spectral properties of a Sturm-Liouville problem with transmission conditions and eigenparameter dependent boundary conditions with retarded argument
Serkan Araci, Mehmet Acikgoz, Azad Bayramov +1
In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities…
On the Identities Involving Special Polynomials Arising From Point of View of Fractional Calculus
Serkan Araci, Erdoğan Şen, Mehmet Acikgoz +1
In the present paper, we investigate some interesting properties including several special polynomials arising from Caputo-fractional derivative. From our investigation, we derive…
Existence and uniqueness of positive solutions of boundary-value problems for fractional differential equations with p-Laplacian operator
Erdoğan Şen, Mehmet Acikgoz, Jong Jin Seo +2
In this article, we consider the boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator. By the properties of Green function and Schauder fi…
p-adic interpolation function related to multiple generalized Genocchi numbers
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
In the present paper, we deal with multiple generalized Genocchi numbers and polynomials. Also, we introduce analytic interpolating function for the multiple generalized Genocchi n…
A note on the modified q-Dedekind sums
Serkan Araci, Erdoğan Şen, Mehmet Acikgoz
In the present paper, the fundamental aim is to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order modified Dedekind-type sums…
A note on the q-Dedekind-type Daehee-Changhee sums with weight alpha arising from modified q-Genocchi polynomials with weight alpha
Serkan Araci, Mehmet Acikgoz, Ayhan Esi
In the present paper, our objective is to treat a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Dedekind-type sums with weight in co…
Extended q-Dedekind-type Daehee-Changhee sums associated with Extended q-Euler polynomials
Serkan Araci, Mehmet Acikgoz
In the present paper, our goal is to introduce a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order dedekind-type sums with weight alpha…
Extended Fermionic p-Adic q-Integrals On Zp In Connection With Applications Of Umbral Calculus
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
The purpose of this paper is to derive some applications of umbral calculus by using extended fermionic p-adic q-integral on Zp. From those applications, we derive some new interes…
A New Approach to Multivariate q-Euler polynomials by using Umbral calculus
Serkan Araci, Xiangxing Kong, Mehmet Acikgoz +1
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
Identities involving q-Genocchi numbers and polynomials
Serkan Araci, Mehmet Acikgoz, Hassan Jolany +1
In this paper, we focus on the q-Genocchi numbers and polynomials. We shall introduce new identities of the q-Genocchi numbers and polynomials by using the fermionic p-adic integra…
Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for…
Dirichlet's type of twisted Eulerian polynomials in connection with Eulerian-L-function
Serkan Araci, Mehmet Acikgoz
In the present paper, we effect Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-integral on the p-adic integer ring. Also, we introduce some new intere…
Asymptotic expressions of eigenvalues and fundamental solutions of a discontinuous fourth-order boundary value problem
Erdoğan Şen, Serkan Araci, Mehmet Acikgoz
In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point.…
New Generalization of Eulerian polynomials and their applications
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials,…