150 citations · 305 across the 41 of their papers we have counts for
10 papers · 1 filter
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…