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: 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: 14
Citation - Scopus: 16
An 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 Üniversitesi
The 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.
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: 17
Citation - Scopus: 19
Achieving More Precise Bounds Based on Double and Triple Integral as Proposed by Generalized Proportional Fractional Operators in the Hilfer Sense
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Al-Qurashi, Maysaa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Cebysev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Cebysev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.
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: 32
Citation - Scopus: 35
Age-Based Analysis of Heart Rate Variability (Hrv) for Patients With Congestive Heart Failure
(World Scientific Publ Co Pte Ltd, 2021) Baleanu, Dumitru; Krejcar, Ondrej; Namazi, Hamidreza; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
It is known that heart activity changes during aging. In this paper, we evaluated alterations of heart activity from the complexity point of view. We analyzed the variations of heart rate of patients with congestive heart failure that are categorized into four different age groups, namely 30-39, 50-59, 60-69, and 70-79 years old. For this purpose, we employed three complexity measures that include fractal dimension, sample entropy, and approximate entropy. The results showed that the trend of increment of subjects' age is reflected in the trend of increment of the complexity of heart rate variability (HRV) since the values of fractal dimension, approximate entropy, and sample entropy increase as subjects get older. The analysis of the complexity of other physiological signals can be further considered to investigate the variations of activity of other organs due to aging.
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: 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: 14
Citation - Scopus: 16
Analysis and Application Using Quad Compound Combination Anti-Synchronization on Novel Fractional-Order Chaotic System
(Springer Heidelberg, 2021) Trikha, Pushali; Baleanu, Dumitru; Jahanzaib, Lone Seth; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, a novel fractional-order chaotic model has been investigated. The characteristic dynamics of the model have been investigated using various tools such as Lyapunov dynamics, bifurcation diagrams, equilibrium point analysis, Kaplan York dimension, existence and uniqueness of solution. The Lyapunov spectrum, bifurcation diagrams and attractors are discussed over a range of fractional order of 0.8 to 1. The considered system is synchronized by using a novel technique quad compound combination anti-synchronization using two control methods, viz. nonlinear and adaptive sliding mode technique. The obtained results of synchronization are compared with some existing literature and also illustrated its application in secure communication.
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/).
Citation - WoS: 4
Citation - Scopus: 5
Analysis of a Coupled System of Nonlinear Fractional Langevin Equations With Certain Nonlocal and Nonseparated Boundary Conditions
(Hindawi Ltd, 2021) Al-Mdallal, Qasem M.; Jarad, Fahd; Laadjal, Zaid; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss-Seidel method in order to solve some specific particular cases of the system.
Citation - WoS: 23
Citation - Scopus: 28
Analysis of a Fractional Order Bovine Brucellosis Disease Model With Discrete Generalized Mittag-Leffler Kernels
(Elsevier, 2023) Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; Attia, Nourhane; Hassan, Ahmed M.; Farman, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness's increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana-Baleanu fractional difference operator of the Liouville-Caputo type. An analysis of the suggested system's well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.

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