Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - WoS: 26
Citation - Scopus: 31
Asymptotic Solutions of Fractional Interval Differential Equations With Nonsingular Kernel Derivative
(Amer inst Physics, 2019) Ahmadian, A.; Salimi, M.; Ferrara, M.; Baleanu, D.; Salahshour, S.
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing.
Citation - WoS: 2
Citation - Scopus: 2
Comment on "maxwell's Equations and Electromagnetic Lagrangian Density in Fractional Form" [J. Math. Phys. 53, 033505 ( 2012)]
(Amer inst Physics, 2014) Al-Jamel, A.; Widyan, H.; Baleanu, D.; Rabei, Eqab M.
In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)]. (C) 2014 AIP Publishing LLC.
Compatibility of Non-Generic Supersymmetries and Geometric Duality for a Subclass of Generalized Pp-Wave Metrics
(Amer inst Physics, 2004) Baleanu, D; Baleanu, Dumitru; Baskal, S; Matematik
Spinning point particle theories accommodate non-generic supercharges in connection with the existence of Killing-Yano tensors. Killing-Yano tensors of order two and three and their corresponding Killing tensors are found for a subclass of generalized pp-wave metrics. These metrics include the pp-wave itself, its possible generalizations and the Siklos metric which is conformal to that. The compatibility between geometric duality and non-generic symmetries is discussed within the context of the metric solutions. It is found that some of the metric solutions admit anti-de Sitter spacetimes while some are found to be purely radiative.
Citation - WoS: 1
Citation - Scopus: 1
Dualization of the Principal Sigma Model
(Amer inst Physics, 2008) Yilmaz, Nejat T.
The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualization of the algebra and the field content of the theory the field equations which are solely written in terms of the field strengths are realized through an extended symmetry algebra parametrization. The structure of this symmetry algebra is derived so that it generates the realization of the field equations in a Bianchi identity of the current derived from the extended parametrization. (c) 2008 American Institute of Physics.
Citation - WoS: 79
Citation - Scopus: 94
Existence and Uniqueness Theorem for a Class of Delay Differential Equations With Left and Right Caputo Fractional Derivatives
(Amer inst Physics, 2008) Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd
The existence and uniqueness theorems for functional right-left delay. and left-right advanced fractional functional differential equations with bounded delay and advance, respectively, are proved. The continuity with respect to the initial function for these equations is also proved under some Lipschitz kind conditions. The Q-operator is used to transform the delay-type equation to an advanced one and vice versa. An example is given to clarify the results. (C) 2008 American Institute Of Physics.
Citation - WoS: 79
Citation - Scopus: 88
Existence Theory and Numerical Solutions To Smoking Model Under Caputo-Fabrizio Fractional Derivative
(Amer inst Physics, 2019) Shah, Kamal; Zaman, Gul; Jarad, Fahd; Khan, Sajjad Ali
In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab. Published under license by AIP Publishing.
Fractals Arising From Newton's Method
(Amer inst Physics, 2012) Cilingir, Figen
We consider the dynamics as a special class of rational functions that are obtained from Newton's method when applied to a polynomial equation. Finding solutions of these equations leads to some beautiful images in complex functions. These images represent the basins of attraction of roots of complex functions. We seek the answer "What is the dynamics near the chosen parabolic fixed points?". In addition, we will provide a detailed history of Fractal and Dynamical System Theory.
Citation - WoS: 15
Citation - Scopus: 18
Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics
(Amer inst Physics, 2011) Vacaru, Sergiu I.; Baleanu, Dumitru
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and associated solitonic hierarchies. The constructions yield horizontal/vertical pairs of fractional vector sine-Gordon equations and fractional vector mKdV equations when the hierarchies for corresponding curve fractional flows are described in explicit forms by fractional wave maps and analogs of Schrodinger maps. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589964]
Citation - WoS: 2
Fractional Euler-Lagrange Equations for Constrained Systems
(Amer inst Physics, 2004) Avkar, Tansel; Avkar, T; Baleanu, D; Baleanu, Dumitru; Matematik
The fractional calculus is the name for the theory of integrals and derivatives of arbitrary order, which generalize the notions of n-fold integration and integer-order differentiation. Differential equations of fractional order appear in certain applied problems and in theoretical researches. In this paper, the Euler-Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus. Two examples of constrained systems possessing a gauge invariance are investigated in details, the explicit solutions of Euler-Lagrange equations are obtained, and the recovery of the classical results is discussed.
Citation - WoS: 179
Citation - Scopus: 192
Fractional Modeling of Blood Ethanol Concentration System With Real Data Application
(Amer inst Physics, 2019) Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; Qureshi, Sania
In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations. Published under license by AIP Publishing.
Citation - WoS: 29
Citation - Scopus: 28
The General Bilinear Techniques for Studying the Propagation of Mixed-Type Periodic and Lump-Type Solutions in a Homogenous-Dispersive Medium
(Amer inst Physics, 2020) Osman, Mohamed S.; Zhu, Wen-Hui; Zhou, Li; Baleanu, Dumitru; Liu, Jian-Guo
This paper aims to construct new mixed-type periodic and lump-type solutions via dependent variable transformation and Hirota's bilinear form (general bilinear techniques). This study considers the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a homogeneous medium in fluid dynamics. The obtained solutions contain abundant physical structures. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D plots.
Citation - WoS: 1
Citation - Scopus: 2
A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering
(Amer inst Physics, 2018) Akgul, Ali; Faraz, Naeem; Inc, Mustafa; Akgul, Esra Karatas; Baleanu, Dumitru; Khan, Yasir
In this paper, a highly nonlinear equations are treated analytically via homotopy perturbation method for fluid mechanics problem. The non-linear differential equations are transformed to a coupled non-linear ordinary, differential equations via similarity transformations. Graphical results are presented and discussed for various physical parameters.
Citation - WoS: 2
Citation - Scopus: 1
Invariant Investigation on the System of Hirota-Satsuma Coupled Kdv Equation
(Amer inst Physics, 2018) Balmeh, Z.; Akgul, A.; Akgul, E. K.; Baleanu, D.; Hashemi, M. S.
We show how invariant subspace method can be extended to the system time fractional differential equations and construct their exact solutions. Effectiveness of the method has been illustrated by the time fractional Hirota-Satsuma Coupled KdV(HSCKdV) equation.
Killing-Yano Tensors, Surface Terms and Superintegrable Systems
(Amer inst Physics, 2004) Baleanu, Dumitru; Baleanu, D; Defterli, Ö; Defterli, Özlem; Matematik
Killing-Yano and Killing tensors are investigated corresponding to a set of two dimensional superintegrable systems. A suitable surface term is added to the corresponding free Lagrangian describing the motion of a particle on a 2-sphere of unit radius and we analyze the symmetries of the obtained geometries.
Citation - WoS: 13
Citation - Scopus: 12
Magnetohydrodynamic Mixed Convection Flow of Jeffery Fluid With Thermophoresis, Soret and Dufour Effects and Convective Condition
(Amer inst Physics, 2019) Baleanu, Dumitru; Husnine, S. M.; Shabbir, Khurram; Iftikhar, Nazish
The aim of this paper is to investigate heat and mass transfer of Jeffery fluid on a stretching sheet. Moreover, the influence of magnetic field with mixed convection, convective boundary condition and Soret and Dufour effects is also brought into the consideration along with chemical reaction and thermophoresis condition. The problem is modeled by system of partial differential equations and solutions are obtained by optimal homotopy analysis method. In addition, for comprehensive interpretation of the influence of the system parameters results are shown by graphs and tables. (C) 2019 Author(s).
Citation - WoS: 45
Citation - Scopus: 42
Mathematical Modeling for Adsorption Process of Dye Removal Nonlinear Equation Using Power Law and Exponentially Decaying Kernels
(Amer inst Physics, 2020) Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; Qureshi, Sania
In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter chi , where 0 < chi <= 1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model's solution in non-integer-order settings. From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained. Published under license by AIP Publishing.
Citation - WoS: 172
Citation - Scopus: 182
A New and Efficient Numerical Method for the Fractional Modeling and Optimal Control of Diabetes and Tuberculosis Co-Existence
(Amer inst Physics, 2019) Ghanbari, Behzad; Baleanu, Dumitru; Jajarmi, Amin
The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.
Citation - WoS: 132
Citation - Scopus: 130
New Fractional Derivatives With Non-Singular Kernel Applied To the Burgers Equation
(Amer inst Physics, 2018) Atangana, Abdon; Baleanu, Dumitru; Saad, Khaled M.
In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively. The results are very effective and accurate. Published by AIP Publishing.
Citation - WoS: 301
Citation - Scopus: 328
A New Fractional Model and Optimal Control of a Tumor-Immune Surveillance With Non-Singular Derivative Operator
(Amer inst Physics, 2019) Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; Baleanu, D.
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined. Published under license by AIP Publishing.
Citation - WoS: 237
Citation - Scopus: 247
New Variable-Order Fractional Chaotic Systems for Fast Image Encryption
(Amer inst Physics, 2019) Deng, Zhen-Guo; Baleanu, Dumitru; Zeng, De-Qiang; Wu, Guo-Cheng
New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor-corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly. Published under license by AIP Publishing.

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