Fen - Edebiyat Fakültesi
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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 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 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 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 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(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 novelweak fuzzy solution for fuzzy linear system(2016) Salahshour, Soheil; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThis article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.Article A pair of Köthe spaces between which all continuous linear operators are bounded(2004) Abdeljawad, Thabet; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiArticle A Prelımınary Work On Investıgatıng Unıted Natıons’s Egovernment Crıterıa In Mıddle East Countrıes(2017) Hussein, Mohammed; Pusatlı, O. Tolga; 51704; 03.07. Yönetim Bilişim Sistemleri; 03. İktisadi ve İdari Birimler Fakültesi; 01. Çankaya ÜniversitesiThe benefits of e-government initiatives empowered by the information and communication technologies, are acknowledged widely with assessment criteria published by the United Nations regularly over the last 15 years. One of the reasons that United Nations has taken such assessment into agenda is the apparent advantages of such initiatives over the citizen, society and government. In parallel literature review and current status of Middle East countries, these issues are investigated with examples: Internet users, awareness and training, culture, intention to use e-government applications of the citizens, portal and interoperability. It is noted that assessment of human capital indices for these countries should be read carefully while considering these topics. The findings reveal the impact of human capital index on evaluating egovernment performance; geographical area and population also affect the adoption of e-government. For this, follow-up work is suggested to investigate the level of information and communication technology and computer literacy along with these factors in the region. This research has limitations which include the sources of information, exclusive economic and legal issues and a number of measurement methods.Article A Result On A Pata-Ciric Type Contraction At A Point(MDPI AG, 2020) Karapınar, Erdal; Fulga, Andreea; Rakoˇcevi´c, Vladimir; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn this manuscript, we define a new contraction mapping, Pata-Cirictype contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ciric. We proved that in a complete space, each Pata-Cirictype contraction at a point possesses a fixed point. We express an example to illustrate the observed result.Article Citation - WoS: 19Citation - Scopus: 21About Maxwell's Equations on Fractal Subsets of R3(de Gruyter Poland Sp Z O O, 2013) Golmankhaneh, Ali K.; Baleanu, Dumitru; Golmankhaneh, Alireza K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn this paper we have generalized -calculus for fractals embedding in a"e(3). -calculus is a fractional local derivative on fractals. It is an algorithm which may be used for computer programs and is more applicable than using measure theory. In this Calculus staircase functions for fractals has important role. -fractional differential form is introduced such that it can help us to derive the physical equation. Furthermore, using the -fractional differential form of Maxwell's equations on fractals has been suggested.Article Citation - WoS: 3Citation - Scopus: 6About the Existence Results of Fractional Neutral Integrodifferential Inclusions With State-Dependent Delay in Frechet Spaces(Hindawi Ltd, 2016) Baleanu, Dumitru; Selvarasu, Siva; Arjunan, Mani Mallika; Suganya, Selvaraj; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiA recent nonlinear alternative for multivalued contractions in Frechet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis.Article Citation - WoS: 1Citation - Scopus: 2Absolutely Stable Difference Scheme for a General Class of Singular Perturbation Problems(Springer, 2020) Alotaibi, A. M.; Ebaid, Abdelhalim; Baleanu, Dumitru; Machado, Jose Tenreiro; Hamed, Y. S.; El-Zahar, Essam R.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThis paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.Article Citation - WoS: 38Citation - Scopus: 46Abundant Distinct Types of Solutions for the Nervous Biological Fractional Fitzhugh-Nagumo Equation Via Three Different Sorts of Schemes(Springer, 2020) Khater, Mostafa M. A.; Baleanu, Dumitru; Khalil, E. M.; Bouslimi, Jamel; Omri, M.; Abdel-Aty, Abdel-Haleem; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThe dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana-Baleanu (AB) time-fractional FitzHugh-Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model's applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.Article Citation - WoS: 34Citation - Scopus: 38Abundant Periodic Wave Solutions for Fifth-Order Sawada-Kotera Equations(Elsevier, 2020) Awan, Aziz Ullah; Osman, Mohamed S.; Baleanu, Dumitru; Alqurashi, Maysaa M.; Tahir, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn this manuscript, two nonlinear fifth-order partial differential equations, namely, the bidirectional and 2D-Sawada-Kotera equations are analytically treated using an extended form of homoclinic process. In the presence of a bilinear form, novel periodic waves with different categories including periodic soliton, solitary and kinky solitary wave solutions are constructed. In the meantime, The diverse features and mechanical qualities of these acquired solutions are elucidated by 3D figures and some contour plots.Article Citation - WoS: 14Citation - Scopus: 16An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations(Wiley-hindawi, 2017) Salahshour, S.; Ahmadian, A.; Ismail, F.; Baleanu, D.; Bishehniasar, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThe demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems.Article Accurate novel explicit complex wave solutions of the (2+1)-dimensional Chiral nonlinear Schrodinger equation(2021) Alshahrani, B.; Yakout, H. A.; Khater, Mostafa M. A.; Abdel-Aty, Abdel-Haleem; Mahmoud, Emad E.; Baleanu, Dumitru; Eleuch, Hichem; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThis manuscript investigates the accuracy of the solitary wave solutions of the (2+1)-dimensional nonlinear Chiral Schrodinger ((2+1)-D CNLS) equation that are constructed by employing two recent analytical techniques (modified Khater (MKhat) and modified Jacobian expansion (MJE) methods). This investigation is based on evaluating the initial and boundary conditions through the obtained analytical solutions then employing the Adomian decomposition (AD) method to evaluate the approximate solutions of the (2+1)-D CNLS equation. This framework gives the ability to get large complex traveling wave solutions of the considered model and shows the superiority of the employed computational schemes by comparing the absolute error for each of them. The handled model describes the edge states of the fractional quantum hall effect. Many novel solutions are obtained with various formulas such as trigonometric, rational, and hyperbolic to the studied model. For more illustration of the results, some solutions are displayed in 2D, 3D, and density plots.Article Citation - WoS: 9Citation - Scopus: 10An Accurate Predictor-Corrector Nonstandard Finite Difference Scheme for an Seir Epidemic Model(Hindawi Ltd, 2020) Ahmad, Riaz; Farooqi, Rashada; Alharbi, Sayer O.; Baleanu, Dumitru; Rafiq, Muhammad; Ahmad, M. O.; Farooqi, Asma; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThe present work deals with the construction, development, and analysis of a viable normalized predictor-corrector-type nonstandard finite difference scheme for the SEIR model concerning the transmission dynamics of measles. The proposed numerical scheme double refines the solution and gives realistic results even for large step sizes, thus making it economical when integrating over long time periods. Moreover, it is dynamically consistent with a continuous system and unconditionally convergent and preserves the positive behavior of the state variables involved in the system. Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge-Kutta (RK) and Euler method of a predictor-corrector type.
