Fen - Edebiyat Fakültesi
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Article Citation - WoS: 79Citation - Scopus: 82The (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 ÜniversitesiThe 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.Article Citation - WoS: 19Citation - Scopus: 23The (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation and Its Optical Solitons(Amer inst Mathematical Sciences-aims, 2021) Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; Baleanu, Umitru; 56389; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat FakültesiA comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrodinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.Article Citation - WoS: 4Citation - Scopus: 32d 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 ÜniversitesiHamilton-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.Article A 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.Article 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 ÜniversitesiThe 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.Article 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 ÜniversitesiThe 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 minihedralArticle 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 ÜniversitesiThis 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.Article A Critical Review of the Joker Movie in the Context of Mahler's Separation-İndividuatin theory and PTSD(2021) Güven, Ayşenur; Işık, Selin; Oya, Sera; Yaşar, Nuray; Topcu Bulut, Merve; 02.04. Psikoloji; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiBu çalışmada Mahler’in ayrılma-bireyleşme kuramı çerçevesinde Joker filmindeki Arthur Fleck karakterinin gelişim evreleri hakkında çıkarımlar yapılması, ilk 36 aylık deneyimlerinin Arthur’un duygu, düşünce ve kişilik gelişimindeki etkilerinin incelenmesi amaçlanmıştır. Mahler’in kuramına göre bireyin ilk altı ayı normal otistik ve normal ortakyaşamsal olmak üzere, birbirinin devamı ve tamamlayıcısı niteliğindeki iki kritik evreden oluşmaktadır. Devamında ise farklılaşma, alıştırma, yeniden yakınlaşma ve bireyliğin pekişmesi ve coşkusal nesne sürekliliğinin başlangıcı olmak üzere dört farklı altevreden oluşan ayrılma-bireyleşme süreci gelmektedir. Kişilik oluşumu sürecinde bu altevreler büyük önem taşımaktadır. Arthur’un narsistik ve madde kötüye kullanım tanısı almış olan annesi ile ilişkisi, baba kavramının eksikliği, çevresiyle olan etkileşimi ve toplum içinde görünür olma arzusu üzerinde durulmuştur. Çocukluk çağında istismar ve ihmale uğrayan, yetişkinlik çağında ise sistematik olarak psikolojik şiddete maruz kalmaya devam eden Arthur'un örseleyici yaşam öyküsü kimlik oluşumunu, sosyal uyumunu, kişilik gelişimini olumsuz etkilemiş ve örselenme sonrası gerginlik bozukluğu (ÖSGB) belirtilerinin oluşmasına yol açmıştır. Bahsedilen bilgiler ışığında Arthur Fleck karakteri, DSM-5 örselenme sonrası gerginlik bozukluğu tanı kriterlerinden faydalanılarak Mahler’in ayrılma-bireyleşme kuramı çerçevesinde incelenmiştir.Article 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 ÜniversitesiLiterature 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.Article 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 ÜniversitesiThere is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.Article A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model(2021) Sweilam, N. H.; Al-Mekhlafi, S. M.; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn this paper, a new stochastic fractional Coronavirus (2019-nCov) model with modified parameters is presented. The proposed stochastic COVID-19 model describes well the real data of daily confirmed cases in Wuhan. Moreover, a novel fractional order operator is introduced, it is a linear combination of Caputo's fractional derivative and Riemann-Liouville integral. Milstein's higher order method is constructed with the new fractional order operator to study the model problem. The mean square stability of Milstein algorithm is proved. Numerical results and comparative studies are introduced.Article A k-Dimensional System of Fractional Finite Difference Equations(2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiWe investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.Article 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 ÜniversitesiWe 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)Article A modified Laplace transform for certain generalized fractional operators(2018) Jarad, Fahd; Thabet, Abdeljawad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIt 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 operatorsArticle 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 ÜniversitesiIn 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.Article A New Class of Contraction in b -Metric Spaces and Applications(2017) Kaushik, P.; Kumar, S.; Kenan, Taş; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiA novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. © 2017 Preeti Kaushik et al.Article A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions(Hindawi LTD, 2014) Wang, Guotao; Liu, Sanyang; Zhang, Lihong; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiA new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.Article 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 ÜniversitesiIn 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.Article A note on (p, q)-analogue type of Fubini numbers and polynomials(2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn 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.p>
Article 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 ÜniversitesiIn 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.
