Yazar "Açıkgöz, Mehmet" için listeleme
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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 ... -
A class of sturm-liouville operators with eigenparameter dependent boundary and transmission conditions
In this study, we investigate a Sturm-Liouville type problem with eigenparameter dependent boundary conditions and eigenparameter dependent transmission conditions. By establishing a new self-adjoint operator A associated ... -
Discontinuous two-point boundary value problems with eigenparameter in the boundary conditions
In the present paper, we deal with discontinuous two-point boundary value problems with eigenparameter in the boundary conditions with transmission conditions at the three points of discontinuities. We obtain asymptotic ... -
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) = ... -
Identities involving some new special polynomials arising from the applications of fractional calculus
Aracı, Serkan; Şen, Erdoğan; Açıkgöz, Mehmet; Oruçoğlu, Kamil (Natural Sciences Publishing Co., 2015)Inspired by a number of recent investigations, we introduce the new analogues of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, the Apostol-Genocchi polynomials based on Mittag-Leffler function. Making ... -
Identities involving the (h, q)-Genocchi polynomials and (h,q)-zeta-type function
Bagdasaryan, A.; Şen, Erdoğan; He, Y.; Aracı, Serkan; Açıkgöz, Mehmet (Jangjeon Mathematical Society, 2014)The fundamental objective of this paper is to obtain some interesting properties for (h, q)-Genocchi numbers and polynomials by using the fermionic p-adic q-integral on ?p and mentioned in the paper q-Bernstein polynomials. ... -
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 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 ... -
Some new formulae for genocchi numbers and polynomials involving bernoulli and euler polynomials
Aracı, Serkan; Açıkgöz, Mehmet; Şen, Erdoğan (Hindawi Publishing Corporation, 2014)We give some new formulae for product of two Genocchi polynomials including Euler polynomials and Bernoulli polynomials. Moreover, we derive some applications for Genocchi polynomials to study a matrix formulation. © 2014 ... -
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 ...