ORCID "0000-0002-3950-6864" Fen Edebiyat Fakültesi Koleksiyonu için listeleme
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Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument
Şen, Erdoğan; Seo, Jong Jin; Aracı, Serkan (Hindawi Ltd, 2013)In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the ... -
Asymptotic properties of a new Sturm-Liouville problem with retarded argument
Şen, Erdoğan; Aracı, Serkan; Açıkgöz, Mehmet (Wiley, 2014)In this work, we study the asymptotic properties of a new Sturm-Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered ... -
A Class of Generating Functions for a New Generalization of Eulerian Polynomials with their Interpolation Functions
Araci, Serkan; Şen, Erdoğan; Açıkgöz, Mehmet (Univ Nis, Fac Sci Math, 2016)Motivated by a number of recent investigations, we define and investigate the various properties of a new family of the Eulerian polynomials. We derive useful results involving these Eulerian polynomials including (for ... -
Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p-Laplacian operator
Araci, Serkan; Şen, Erdoğan; Açıkgöz, Mehmet; Srivastava, Hari M. (Springeropen, 2015)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 ... -
Existence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations with p-Laplacian Operator and Identities on the Some Special Polynomials
Şen, Erdoğan; Açıkgöz, Mehmet; Seo, Jong Jin; Aracı, Serkan; Oruçoğlu, Kamil (Hindawi Ltd, 2013)We consider the following boundary- value problem of nonlinear fractional differential equation with p-Laplacian operator D-0+(beta)(phi(p)(D(0+)(alpha)u(t))) + a(t)f(u) = 0, 0 < t < 1, u(0) = gamma u(h) + lambda, u'(0) = ... -
A New Approach to Multivariate q-Euler Polynomials Using the Umbral Calculus
Araci, Serkan; Kong, Xiangxing; Açıkgöz, Mehmet; Şen, Erdoğan (Univ Waterloo, 2014)We derive numerous identities for multivariate q- Euler polynomials by using the umbral calculus. -
A note on the modified q-Dedekind sums
Araci, Serkan; Şen, Erdoğan; Açıkgöz, Mehmet (Bulgarian Acad Science, 2013)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 Extended Dedekind-type sums related to q-Genocchi polynomials with ... -
On a p-ADIC interpolating function for the generalized genocchi numbers and its behaviour at s = 0
Araci, Serkan; Şen, Erdoğan (Charles Babbage Res Ctr, 2015)In this work, we consider the generalized Genocchi numbers and polynomials. However, we introduce analytic interpolating function for the generalized Genocchi numbers attached to chi at negative integers in complex plane ... -
On the extended Kim's p-adic q-deformed fermionic integrals in the p-adic integer ring
Araci, Serkan; Açıkgöz, Mehmet; Şen, Erdoğan (Academic Press Inc Elsevier Science, 2013)The purpose of this paper is to derive some applications of umbral calculus by using extended fermionic p-adic q-integral on Z(p). From those applications, we derive some new interesting properties on the new family of ... -
On the von Staudt-Clausen's theorem associated with q-Genocchi numbers
Araci, Serkan; Açıkgöz, Mehmet; Şen, Erdoğan (Elsevier Science Inc, 2014)Recently, the von Staudt-Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt-Clausen's ... -
Spectral Problem for the Sturm-Liouville Operator with Retarded Argument Containing a Spectral Parameter in the Boundary Condition
Şen, Erdoğan; Açıkgöz, Mehmet; Aracı, Serkan (Springer, 2017)We consider a discontinuous Sturm-Liouville problem with retarded argument containing a spectral parameter in the boundary condition. First, we investigate the simplicity of eigenvalues and then prove the existence theorem. ... -
Theorems on Genocchi Polynomials of Higher Order Arising From Genocchi Basis
Araci, Serkan; Şen, Erdoğan; Açıkgöz, Mehmet (Mathematical Soc Rep China, 2014)Recently, Kim et al. [8] constructed a new method to obtain interesting identities related to Euler polynomials of higher order arising from Euler basis. In the present paper, we study to Genocchi polynomials of higher ...