Fen - Edebiyat Fakültesi

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Citation - WoS: 19
Citation - Scopus: 23
The (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 Fakültesi
A 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.
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: 3
Citation - Scopus: 6
About 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 Üniversitesi
A 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.
Citation - WoS: 1
Citation - Scopus: 2
Absolutely 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 Üniversitesi
This 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.
Citation - WoS: 38
Citation - Scopus: 46
Abundant 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 Üniversitesi
The 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.
Citation - WoS: 34
Citation - Scopus: 38
Abundant 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 Üniversitesi
In 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.
Citation - WoS: 9
Citation - Scopus: 10
An 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 Üniversitesi
The 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.
Citation - WoS: 11
Citation - Scopus: 11
Additive Trinomial Frechet Distribution With Practical Application
(Elsevier, 2022) Sindhu, Tabassum Naz; Jarad, Fahd; Lone, Showkat Ahmad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This article presents an innovative model called Additive Trinomial Fre chet (ATF) distribution using six parameters. The indicated model is worthy of modeling survival data with a non-monotonic hazard rate. The statistical characteristics of ATF model such as probability generating function, Renyi, Shannon, Tsallis and Mathai-Houbold entropy, quantile function, order statistics, maximum likelihood estimation, factorial and characteristic function, moment generating function, Stress-Strength analysis are thoroughly discussed. The effectiveness of suggested model is demonstrated by the use of a data set from real life. The suggested model has demonstrated better performance and fits the data used superior than other significant counterparts.
Citation - WoS: 14
Citation - Scopus: 9
Advances on the Fixed Point Results Via Simulation Function Involving Rational Terms
(Springer, 2021) Chen, Chi-Ming; Alghamdi, Maryam A.; Fulga, Andreea; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem.
Citation - WoS: 16
Citation - Scopus: 14
An Algorithm for Hopf Bifurcation Analysis of a Delayed Reaction-Diffusion Model
(Springer, 2017) Kayan, S.; Merdan, H.; 49206; 01. Çankaya Üniversitesi
We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the coefficients of the characteristic equation corresponding to linearization of the system. Furthermore, an algorithm to obtain the formulas for determining the direction of the Hopf bifurcation, the stability, and period of the periodic solution is given by using the Poincare normal form and the center manifold theorem. Finally, we give several examples and some numerical simulations to show the effectiveness of the algorithm proposed.
Citation - WoS: 30
Citation - Scopus: 32
All Linear Fractional Derivatives With Power Functions' Convolution Kernel and Interpolation Properties
(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Shiri, Babak; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Our attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions' convolution kernel a(a)(t-s)b(a) of order a a (0,1). We determine analytic functions a(a) and b(a) such that when a-* 0+, the corresponding operator becomes identity operator, and when a-* 1- the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared.
Citation - WoS: 2
Citation - Scopus: 3
Almost Local Stability in Discrete Delayed Chaotic Systems
(Springer, 2017) Baleanu, Dumitru; Taghizadeh, Elham; Gilani, Zahra Goli; Nategh, Mehdi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This work studies dynamic of delayed discrete chaotic systems with bounded and unbounded delays. The time lags appear in additive which is coupled with a smooth function and nonadditive forms. It has been shown that, in both additive and nonadditive cases, the primal (non-delayed) system is neutral to the bounded delay to possess an attractive fixed point. Nevertheless, if a nonadditive and unbounded delay is supposed to affect a chaotic and measure preserving system locally, then the delay function might be sensitive to initial states. A local stabilization to the dynamics of Logistic and Gaussian maps are made and creation of attractive fixed points is illustrated.
Citation - WoS: 27
Citation - Scopus: 27
Almost Periodic Dynamics of a Discrete Nicholson's Blowflies Model Involving a Linear Harvesting Term
(Springer, 2012) Abdeljawad, Thabet; Alzabut, Jehad; Bolat, Yasar; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We consider a discrete Nicholson's blowflies model involving a linear harvesting term. Under appropriate assumptions, sufficient conditions are established for the existence and exponential convergence of positive almost periodic solutions of this model. To expose the effectiveness of the main theorems, we support our result by a numerical example.
Citation - Scopus: 1
Alpha Fractional Frequency Laplace Transform Through Multiseries
(Springer, 2020) Gnanaprakasam, Britto Antony Xavier; Jarad, Fahd; Murugesan, Meganathan; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Our main goal in this work is to derive the frequency Laplace transforms of the products of two and three functions with tuning factors. We propose the Laplace transform for certain types of multiseries of circular functions as well. For use in numerical results, we derive a finite summation formula and m-series formulas. Moreover, we discuss various explanatory examples.
Citation - WoS: 2
Citation - Scopus: 2
Analysing Discrete Fractional Operators With Exponential Kernel for Positivity in Lower Boundedness
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Aydi, Hassen; Hamed, Yasser S.; Mahmood, Sarkhel Akbar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper we study the positivity analysis problems for discrete fractional operators with exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied to a discrete Caputo-Fabrizio-Caputo fractional operator of order omega of another discrete Caputo-Fabrizio-Riemann fractional operator of order beta. Furthermore, the results are obtained for these operators with having the same orders. The conditions for the discrete fractional operators with respect to negative lower bound conditions are expressed in terms of a positive epsilon.
Citation - WoS: 31
Citation - Scopus: 35
Analysis and Applications of the Proportional Caputo Derivative
(Springer, 2021) Baleanu, Dumitru; Akgul, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we investigate the analysis of the proportional Caputo derivative that recently has been constructed. We create some useful relations between this new derivative and beta function. We discretize the new derivative. We investigate the stability and obtain a stability condition for the new derivative.
Citation - WoS: 43
Citation - Scopus: 52
Analysis and Dynamics of Fractional Order Covid-19 Model With Memory Effect
(Elsevier, 2021) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Yadav, Supriya; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The present article attempts to examine fractional order Covid-19 model by employing an efficient and powerful analytical scheme termed as q-homotopy analysis Sumudu transform method (q-HASTM). The q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. Liouville-Caputo approach of the fractional operator has been employed. The proposed modelis also examined numerically via generalized Adams-Bashforth-Moulton method. We determined model equilibria and also give their stability analysis by employing next generation matrix and fractional Routh-Hurwitz stability criterion.
Citation - WoS: 13
Citation - Scopus: 15
Analysis and Numerical Solution of the Generalized Proportional Fractional Cauchy Problem
(Elsevier, 2021) Baleanu, D.; Makhlouf, Abdellatif Ben; Nagy, A. M.; Boucenna, Djalal; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we explore the existence and uniqueness theorem for a problem of the fractional Cauchy form, with dependence on the generalized proportional Caputo derivative. Furthermore, a new numerical technique is presented based on a decomposition formula for the generalized proportional Caputo derivative. Convergence analysis of the proposed technique is proved. Finally, numerical results are obtained to confirm the validity of the proposed method. (C) 2021 IMACS. Published by Elsevier reserved.
Citation - WoS: 4
Citation - Scopus: 11
An Analysis for Klein-Gordon Equation Using Fractional Derivative Having Mittag-Leffler Kernel
(Wiley, 2021) Baleanu, Dumitru; Kumar, Amit; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Within this paper, we present an analysis of the fractional model of the Klein-Gordon (K-G) equation. K-G equation is considered as one of the significant equations in mathematical physics that describe the interaction of soliton in a collision less plasma. In a novel aspect of this work, we have used the latest form of fractional derivative (FCs), which contains the Mittag-Leffler type of kernel. The homotopy analysis transform method (HATM) is being taken to solve the fractional model of the K-G equation. A convergence study of HATM has been studied. The existence and uniqueness of the solution for the fractional K-G equation are presented. For verifying the obtained numerical outcomes regarding accuracy and competency, we have given different graphical presentations. Figures are reflecting that a novel form of the technique is a good organization in respect of proficiency and accurateness to solve the mentioned fractional problem.
Citation - WoS: 28
Citation - Scopus: 31
Analysis of a Conformable Generalized Geophysical Kdv Equation With Coriolis Effect
(Elsevier, 2023) Fatima, Nahid; Abdelmohsen, Shaimaa A. M.; Alanazi, Meznah M.; Ahmad, Shabir; Baleanu, Dumitru; Saifullah, Sayed; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, we study new solutions of generalized version of geophysical KdV equation which is called generalized perturbed KdV (gpKdV) under time-space conformable oper-ator. We implement two methods to get some novel waves solution of the gpKdV equation. First, we use extended Tanh-method to extract new solutions of considered equations in the form of trigonometric hyperbolic functions. To achieve Sine and Cosine hyperbolic solutions, we use gen-eralized Kudryashov (GK) technique with Riccati equation. We show the behaviour of solutions via 2D and 3D figures. Also, we analyze the Corioles effect on the evolution of waves solutions of the considered equation.CO 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

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