Yantir, Ahmet
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01.01.02.02. Matematik Bölümü
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| Journal | Count |
|---|---|
| Filomat | 2 |
| Applied Mathematics and Computation | 1 |
| Applied Mathematics in Science and Engineering | 1 |
| Bulletin of the Belgian Mathematical Society - Simon Stevin | 1 |
| Demonstratio Mathematica | 1 |
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Article Citation - Scopus: 1Analysis on α-time scales and its applications to Cauchy-Euler equation(Natural Sciences Publishing, 2024) Burcu Silindir; Seçil Gergün; Ahmet Yantir; Gergün, Seçil; Silindir, Burcu; Yantir, AhmetThis article is devoted to present the α-power function calculus on α-time scale the α-logarithm and their applications on α-difference equations. We introduce the α-power function as an absolutely convergent infinite product. We state that the α-power function verifies the fundamentals of α-time scale and adheres to both the additivity and the power rule for α-derivative. Next we propose an α-analogue of Cauchy-Euler equation whose coefficient functions are α-polynomials and then construct its solution in terms of α-power function. As illustration we present examples of the second order α-Cauchy-Euler equation. Consequently we construct α-analogue of logarithm function which is determined in terms of α-integral. Finally we propose a second order BVP for α-Cauchy-Euler equation with two point unmixed boundary conditions and compute its solution by the use of Green’s function. © 2024 Elsevier B.V. All rights reserved.Article Citation - WoS: 7Bessel equation and Bessel function on T(q-h)(Tubitak Scientific & Technological Research Council Turkey, 2022) Ahmet Yantir; Burcu Silindir Yantir; Zehra Tuncer; Yantir, Burcu Silindir; Tuncer, Zehra; Yantir, AhmetThis article is devoted to present nabla (q h)-analogues of Bessel equation and Bessel function. In order to construct series solution of nabla (q h)-Bessel equation we present nabla (q h)-analysis regarding nabla generalized quantum binomial nabla (q h)-analogues of Taylor's formula Gauss's binomial formula Taylor series analytic functions analytic exponential function with its fundamental properties analytic trigonometric and hyperbolic functions. We emphasize that nabla (q h)-Bessel equation recovers classical h- and q-discrete Bessel equations. In addition we establish nabla (q h)-Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate its reductions. Finally we develop modified nabla (q h)-Bessel equation modified nabla (q h)-Bessel function and its relation with nabla (q h)-Bessel function.Article Citation - WoS: 1Citation - Scopus: 10On continuous dependence of solutions of dynamic equations(Elsevier Inc. usjcs@elsevier.com, 2015) Mieczysław Cichoń; Ahmet Yantir; Cichoń, Mieczysław; Yantir, AhmetThe main goal of the paper is to present a new approach to the problem of continuous dependence of solutions of differential or dynamic problems on their domains. This is of particular interests when we use dynamic (difference in particular) equations as discretization of a given one. We cover a standard construction based of difference approximations for the continuous one but we are not restricted only to this case. For a given differential equation we take a sequence of time scales and we study the convergence of time scales to the domain of the considered problem. We choose a kind of convergence of such approximated solutions to the exact solution. This is a step for creating numerical analysis on time scales and we propose to replace in such a situation the difference equations by dynamic ones. In the proposed approach we are not restricted to the case of classical numerical algorithms. Moreover this allows us to find an exact solution for considered problems as a limit of a sequence of solutions for appropriate time scales instead of solving it analytically or calculating approximated solutions for the original problems. © 2015 Elsevier B.V. All rights reserved.Article Citation - WoS: 16Citation - Scopus: 18Generalized quantum exponential function and its applications(University of Nis filomat@pmf.ni.ac.rs, 2019) Burcu Silindir; Ahmet Yantir; Silindir, Burcu; Yantir, AhmetThis article aims to present (q h)-analogue of exponential function which unifies extends h-and q-exponential functions in a convenient and efficient form. For this purpose we introduce generalized quantum binomial which serves as an analogue of an ordinary polynomial. We state (q h)-analogue of Taylor series and introduce generalized quantum exponential function which is determined by Taylor series in generalized quantum binomial. Furthermore we prove existence and uniqueness theorem for a first order linear homogeneous IVP whose solution produces an infinite product form for generalized quantum exponential function. We conclude that both representations of generalized quantum exponential function are equivalent. We illustrate our results by ordinary and partial difference equations. Finally we present a generic dynamic wave equation which admits generalized trigonometric hyperbolic type of solutions and produces various kinds of partial differential/difference equations. © 2020 Elsevier B.V. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 2Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces(De Gruyter Open Ltd peter.golla@degruyter.com, 2015) Ahmet Yantir; Ireneusz Kubiaczyk; Aneta Sikorska-Nowak; Yantir, Ahmet; Kubiaczyk, Ireneusz; Sikorska-Nowak, AnetaIn this paper we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose we introduce an equivalent integral operator to the SLBVP by means of Green's function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of noncompactness we prove the existence of the fixed points of the equivalent integral operator. Mönch's fixed point theorem is used to prove the main result. Finally we also remark that it is straightforward to guarantee the existence of Carathéodory solutions for the SLBVP if Kuratowski measure of noncompactness is replaced by any axiomatic measure of noncompactness. © 2016 Elsevier B.V. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 4Generalized Polynomials and Their Unification and Extension to Discrete Calculus(MDPI, 2023) Mieczyslaw Cichon; Burcu Silindir; Ahmet Yantir; Secil Gergun; Silindir, Burcu; Yantir, Ahmet; Cichoń, Mieczysław; Gergün, SeçilIn this paper we introduce a comprehensive and expanded framework for generalized calculus and generalized polynomials in discrete calculus. Our focus is on (q,h)-time scales. Our proposed approach encompasses both difference and quantum problems making it highly adoptable. Our framework employs forward and backward jump operators to create a unique approach. We use a weighted jump operator alpha that combines both jump operators in a convex manner. This allows us to generate a time scale alpha which provides a new approach to discrete calculus. This beneficial approach enables us to define a general symmetric derivative on time scale alpha which produces various types of discrete derivatives and forms a basis for new discrete calculus. Moreover we create some polynomials on alpha-time scales using the alpha-operator. These polynomials have similar properties to regular polynomials and expand upon the existing research on discrete polynomials. Additionally we establish the alpha-version of the Taylor formula. Finally we discuss related binomial coefficients and their properties in discrete cases. We demonstrate how the symmetrical nature of the derivative definition allows for the incorporation of various concepts and the introduction of fresh ideas to discrete calculus.Article Citation - Scopus: 2Existence of solutions to fractional differential inclusions with p-laplacian operator(Texas State University - San Marcos editor@ejde.math.txstate.edu, 2014) Ahmet Yantir; Fatma Serap Topal; Topal, Fatma Serap; Yantir, AhmetIn this article we are prove the existence of solutions for three-point fractional differential inclusions with p-Laplacian operator. We use fixed point theory for set valued upper semi-continuous maps for obtaining the solutions. © 2014 Elsevier B.V. All rights reserved.Article Citation - WoS: 12EXISTENCE OF SOLUTIONS OF THE DYNAMIC CAUCHY PROBLEM IN BANACH SPACES(DE GRUYTER POLAND SP Z O O, 2012) Mieczyslaw Cichon; Ireneusz Kubiaczyk; Aneta Sikorska-Nowak; Ahmet Yantir; Yantir, Ahmet; Cichon, Mieczyslaw; Kubiaczyk, Ireneusz; Sikorska-Nowak, AnetaIn this paper we obtain the existence of solutions and Caratheodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales x(triangle)(t) = f(tx(t)) x(0)=x(o) t is an element of I-a where f is continuous or f satisfies Caratheodory conditions and some conditions expressed in terms of measures of noncompactness. The Manch fixed point theorem is used to prove the main result which extends these obtained for real valued functions.Article Citation - WoS: 3Citation - Scopus: 3Power function and binomial series on T(q-h)(TAYLOR & FRANCIS LTD, 2023) Secil Gergun; Burcu Silindir; Ahmet Yantir; Gergün, Seçil; Silindir, Burcu; Yantir, AhmetThis article is devoted to present (q h) -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla (q h) -power function we present (q h)-analogue of binomial series and conclude that such power function is (q h)-analytic. We prove the analyticity by showing that both the power function and its absolutely convergent Taylor series solve the same IVP. Finally we present the reductions of (q h)-binomial series to classical binomial series Gauss' binomial and Newton's binomial formulas.Article Citation - Scopus: 8Bessel equation and Bessel function on $\\mathbb{T}(q h)$(Tubitak, 2022) Ahmet Yantir; BURCU SILINDIR YANTIR; Zehra TUNCER; Yantır, Burcu Sılındır; Tuncer, Zehra; Yantir, AhmetThis article is devoted to present nabla $(q h)$ -analogues of Bessel equation and Bessel function. In order to construct series solution of nabla $(q h)$ -Bessel equation we present nabla $(q h)$ -analysis regarding nabla generalized quantum binomial nabla $(q h)$ -analogues of Taylor’s formula Gauss’s binomial formula Taylor series analytic functions analytic exponential function with its fundamental properties analytic trigonometric and hyperbolic functions. We emphasize that nabla $(q h)$ -Bessel equation recovers classical $h-and q-discrete$ Bessel equations. In addition we establish nabla $(q h)4 -Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate its reductions. Finally we develop modified nabla $(q h)$ -Bessel equation modified nabla $(q h)$ -Bessel function and its relation with nabla $(q h)$ -Bessel function.
