Matematik Bölümü

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Citation - WoS: 79
Citation - Scopus: 82
The (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation: Its Solitons and Jacobi Elliptic Function Solutions
(Springer Heidelberg, 2021) Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; Hosseini, Kamyar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2+1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
Citation - WoS: 4
Citation - Scopus: 3
2d Gravity and the Hamilton-Jacobi Formalism
(Soc Italiana Fisica, 2002) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Hamilton-Jacobi formalism is used to study 2D gravity and its SL(2, R) hidden symmetry. If the contribution of the surface term is considered, the obtained results coincide with those given by the Dirac and Faddeev-Jackiw approaches.
A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The result of Ćirić [1] on a common fixed point theorem of Greguš type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral.
A common fixed point theorem of a Gregus type on convex cone metric spaces
(Eudoxus Press, 2011) Abdeljawad, Thabet; Karapınar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The result of Ciric [1] on a common fixed point theorem of Gregus-type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral
A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
(Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.
A Discussion On the Role of People in Global Software Development [Rasprava O Ulozi Ljudi U Globalnom Razvoju Softvera]
(2013) Misra, Sanjay; Colomo-Palacios, Ricardo; Pusatlı, Özgür Tolga; Soto-Acosta, Pedro; 51704; 03.07. Yönetim Bilişim Sistemleri; 03. İktisadi ve İdari Birimler Fakültesi; 01. Çankaya Üniversitesi
Literature is producing a considerable amount of papers which focus on the risks, challenges and solutions of global software development (GSD). However, the influence of human factors on the success of GSD projects requires further study. The aim of our paper is twofold. First, to identify the challenges related to the human factors in GSD and, second, to propose the solution(s), which could help in solving or reducing the overall impact of these challenges. The main conclusions of this research can be valuable to organizations that are willing to achieve the quality objectives regarding GSD projects.
A Gap in the Paper A Note On Cone Metric Fixed Point Theory and Its Equivalence [Nonlinear Anal. 72(5), (2010), 2259-2261]
(2011) Abdeljawad, Thabet; Karapınar, Erdal; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.
A Kamenev-type oscillation result for a linear (1+alpha)-order fractional differential equation
(Elsevier Science Inc., 2015) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1)
A modified Laplace transform for certain generalized fractional operators
(2018) Jarad, Fahd; Thabet, Abdeljawad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
It is known that Laplace transform converges for functions of exponential order. In order to extend the possibility of working in a large class of functions, we present a modified Laplace transform that we call ρ-Laplace transform, study its properties and prove its own convolution theorem. Then, we apply it to solve some ordinary differential equations in the frame of a certain type generalized fractional derivatives. This modified transform acts as a powerful tool in handling the kernels of these generalized fractional operators
A new algorithm for solving dynamic equations on a time scale
(2017) Jafari, H.; Haghbin, A.; Johnston, S. J.; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose a numerical algorithm to solve a class of dynamic time scale equation which is called the q-difference equation. First, we apply the method for solving initial value problems (IVPs) which contain the first and second order delta derivatives. Illustrative examples show the usefulness of the method. Then we present applications of the method for solving the strongly non-linear damped q-difference equation. The results show that our method is more accurate than the other existing method. (C) 2016 Elsevier B.V. All rights reserved.
A Note On (P, Q)-Analogue Type of Fubini Numbers and Polynomials
(American Institute of Mathematical Sciences, 2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.
A Note On Non-İnstantaneous Impulsive Fractional Neutral Integro-Differential Systems With State-Dependent Delay in Banach Spaces
(Eudoxus Press, 2018) Suganya, Selvaraj; Baleanu, Dumitru; Kalamani, Palaniyappan; Arjunan, M. Mallika; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this research, we establish the existence results for non-instantaneous impulsive fractional neutral integro-differential systems with state-dependent delay in Banach space. By utilizing the Banach contraction principle and condensing fixed point theorem coupled with semigroup theory, we build up the desired results. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [5]. In the end, an example is given to show the abstract theory.
A note on the chain rule on time scales
(Çankaya Üniversitesi, 2008) Abdeljawad, Thabet; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
It is known, in general, that the chain rule on general time scale derivatives does not behave well as in the case of usual derivative. However, we discuss some special cases where the time scale derivative has the usual chain rule. The results are analyzed for both the delta and nabla time scales derivatives.
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
(Sage Publications LTD, 2017) Ezz-Eldien, S. S.; Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.
About fractional calculus of singular Lagrangians
(IEEE, 2004) Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details.
About fractional quantization and fractional variational principles
(2009) Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
in this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.
Citation - WoS: 64
Citation - Scopus: 70
About Fractional Quantization and Fractional Variational Principles
(Elsevier, 2009) Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
in this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.
Citation - WoS: 20
Citation - Scopus: 24
About Fractional Supersymmetric Quantum Mechanics
(inst Physics Acad Sci Czech Republic, 2005) Muslih, SI; Baleanu, D; 56389; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi
Fractional Euler-Lagrange equations are investigated in the presence of Grassmann variables. The fractional Hamiltonian and the path integral of the fractional supersymmetric classical model are constructed.
About Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
(Amer Soc Mechanical Engineers, 2005) Baleanu, Dumitru; Muslih, Sami I.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
sRecently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal's approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schrodinger equation is presented.
Citation - WoS: 3
Citation - Scopus: 3
About Metafluid Dynamics
(inst Physics Acad Sci Czech Republic, 2004) Baleanu, D; 56389; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi
The analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is investigated as a constrained system within fractional Riemann-Liouville derivatives.

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