WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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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
Difference Discrete Variational Principles
(Amer inst Physics, 2006) Baleanu, Dumitru; Jarad, Fahd
The paper provides the discrete Lagrangian and Hamiltonian formulations of mechanical systems for both non-singular and singular cases. The Lagrangians with linear velocities and with higher velocities are investigated and the corresponding difference Euler-Lagrange equations and Hamiltonians are found.
Differential Algebraic Equations in Primal Dual Interior Point Optimization Methods
(Amer inst Physics, 2004) Kasap, S; Kasap, Suat; Trafalis, TB; Endüstri Mühendisliği
Primal dual Interior Point Methods (IPMs) generate points that lie in the neighborhood of the central trajectory. The key ingredient of the primal dual IPMs is the parameterization of the central trajectory. A new approach to the parameterization of the central trajectory is presented. Instead of parameterizing the central trajectory by the barrier parameter, it is parameterized by the time by describing a continuous dynamical system. Specifically, a new update rule based on the solution of an ordinary differential equation for the barrier parameter of the primal dual IPMs is presented. The resulting ordinary differential equation combined with the first order Karush-Kuhn-Tucker (KKT) conditions, which are algebraic equations, are called differential algebraic equations (DAEs). By solving DAEs, we find an optimal solution to the given problem.
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: 41
Citation - Scopus: 42
Eley-Rideal and Hot Atom Reactions Between Hydrogen Atoms on Ni(100): Electronic Structure and Quasiclassical Studies
(Amer inst Physics, 2001) Guvenc, ZB; Sha, XW; Jackson, B
The reactions of gas-phase H (or D) atoms with D (or H) atoms adsorbed onto a Ni(100) surface are studied. Electronic structure calculations based on density functional theory are used to examine the interaction of H atoms with the Ni(100) surface, as well as the interactions between two H atoms near the metal surface. A model potential-energy surface based on ideas from effective medium theory is fit to the results of these electronic structure calculations. Quasiclassical trajectory methods are used to simulate the interaction of low energy H and D atom beams with H and D-covered Ni(100) surfaces. It is found that hot-atom processes dominate the formation of molecular hydrogen. The distribution of energy in the product molecules is examined with regard to the various pathways available for reaction. The initial adsorbate coverage is varied and is shown to control the relative amounts of reflection, reaction, sticking, and subsurface penetration. Our results are compared with those from similar studies on Cu(111) and available experimental data for Ni(100). (C) 2001 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.
Citation - WoS: 1
Citation - Scopus: 1
Fmml: a Feature Model Markup Language
(Amer inst Physics, 2011) Nabdel, Leili; Karatas, Ahmet Serkan; Oguztuzun, Halit; Dogru, Ali
Feature modeling is a common way of representing commonality and variability in Software Product Line Engineering. Alternative notations are available to represent feature models. Compared with graphical notations, text-based notations can be more amenable to automated processing and tool interoperability. In this paper, we propose an XML-based feature modeling language to represent extended feature models with complex relationships.
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: 11
Citation - Scopus: 10
H(D) → D(H)+cu Collision System: Molecular Dynamics Study of Surface Temperature Effects
(Amer inst Physics, 2011) Vurdu, Can D.; Guvenc, Ziya B.
All the channels of the reaction dynamics of gas-phase H (or D) atoms with D (or H) atoms adsorbed onto a Cu(111) surface have been studied by quasiclassical constant energy molecular dynamics simulations. The surface is flexible and is prepared at different temperature values, such as 30 K, 94 K, and 160 K. The adsorbates were distributed randomly on the surface to create 0.18 ML, 0.28 ML, and 0.50 ML of coverages. The multi-layer slab is mimicked by a many-body embedded-atom potential energy function. The slab atoms can move according to the exerted external forces. Treating the slab atoms non-rigid has an important effect on the dynamics of the projectile atom and adsorbates. Significant energy transfer from the projectile atom to the surface lattice atoms takes place especially during the first impact that modifies significantly the details of the dynamics of the collisions. Effects of the different temperatures of the slab are investigated in this study. Interaction between the surface atoms and the adsorbates is modeled by a modified London-Eyring-Polanyi-Sato (LEPS) function. The LEPS parameters are determined by using the total energy values which were calculated by a density functional theory and a generalized gradient approximation for an exchange-correlation energy for many different orientations, and locations of one-and two-hydrogen atoms on the Cu(111) surface. The rms value of the fitting procedure is about 0.16 eV. Many different channels of the processes on the surface have been examined, such as inelastic reflection of the incident hydrogen, subsurface penetration of the incident projectile and adsorbates, sticking of the incident atom on the surface. In addition, hot-atom and Eley-Rideal direct processes are investigated. The hot-atom process is found to be more significant than the Eley-Rideal process. Furthermore, the rate of subsurface penetration is larger than the sticking rate on the surface. In addition, these results are compared and analyzed as a function of the surface temperatures. (c) 2011 American Institute of Physics. [doi:10.1063/1.3583811]
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: 46
Kinetic Model for Eley-Rideal and Hot Atom Reactions Between H Atoms on Metal Surfaces
(Amer inst Physics, 2002) Jackson, B; Sha, XW; Guvenc, ZB
A simple kinetic model is used to describe the interaction of H and D atomic beams with H- and D-covered metal surfaces. The atoms incident from the gas phase can have a direct Eley-Rideal reaction with an adsorbate, reflect, penetrate into the bulk, knock an adsorbate out of its binding site, or trap to form a hot atom. These hot mobile atoms can go on to react with other adsorbates, or eventually relax and stick. A coarse-graining approach, which takes advantage of the large difference between the time scales for the kinetics experiments and the reaction dynamics, allows us to derive relatively simple kinetic equations for reaction rates and coverages. The approach is similar to a kinetic random walk model developed by Kuppers and co-workers [J. Phys. Chem. 109, 4071 (1998)] except that our equations can be used to derive analytical expressions for saturation coverages, rates, and yields. The model is applied to the case of H atom reactions on a Ni(100) surface, and a detailed comparison is made with both experimental and quasiclassical studies. (C) 2002 American Institute of Physics.

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