Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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A branch and bound algorithm for sector allocation of a naval task group
(Wiley-blackwell, 2011) Karasakal, Orhan; Karasakal, Orhan; Kandiller, Levent; Kandiller, Levent; Ozdemirel, Nur Evin; 5706; 2634
A naval task group (TG) is a collection of naval combatants and auxiliaries that are grouped together for the accomplishment of one or more missions. Ships forming a TG are located in predefined sectors. We define determination of ship sector locations to provide a robust air defense formation as the sector allocation problem (SAP). A robust formation is one that is very effective against a variety of attack scenarios but not necessarily the most effective against any scenario. We propose a 0-1 integer linear programming formulation for SAP. The model takes the size and the direction of threat into account as well as the defensive weapons of the naval TG. We develop tight lower and upper bounds by incorporating some valid inequalities and use a branch and bound algorithm to exactly solve SAP. We report computational results that demonstrate the effectiveness of the proposed solution approach. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 655-669, 2011
A density functional study of bare and hydrogenated platinum clusters
(Elsevier, 2006) Sebetci, Ali; 20965
We perform density functional theory calculations using Gaussian atomic-orbital methods within the generalized gradient approximation for the exchange and correlation to study the interactions in the bare and hydrogenated platinum clusters. The minimum-energy structures, binding energies, relative stabilities. vibrational frequencies and the highest occupied and lowest unoccupied molecular-orbital gaps of PtnHm (n = 1-5, m = 0-2) clusters are calculated and compared with previously studied pure platinum and hydrogenated platinum clusters. We investigate any magic behavior in hydrogenated platinum clusters and find that Pt4H2 is snore stable than its neighboring sizes. The lowest energy structure of Pt-4 is found to be a distorted tetrahedron and that of Pt-5 found to be a bridge site capped tetrahedron which is a new global minimum for Pt-5 cluster. The successive addition of H atoms to Pt-n clusters leads to an oscillatory change in the magnetic moment of Pt-3-Pt-5 clusters. (c) 2006 Elsevier B.V. All rights reserved.
A Freely Damped Oscillating Fractional Dynamic System Modeled By Fractional Euler-Lagrange Equations
(Sage Publications Ltd, 2018) Agila, Adel; Baleanu, Dumitru; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; 56389
The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler-Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.
A generalized q-mittag-leffler function by q-captuo fractional linear equations
(Hindawi Ltd, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Benli, Betul; Baleanu, Dumitru; Baleanu, Dumitru
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo (1995).
A Gronwall inequality via the generalized proportional fractional derivative with applications
(Springer, 2019) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Sudsutad, Weerawat; 234808
In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.
A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems
(Sage Publications Ltd, 2007) Agrawal, Om P.; Baleanu, Dumitru; Baleanu, Dumitru; 56389
This paper deals with a direct numerical technique for Fractional Optimal Control Problems (FOCPs). In this paper, we formulate the FOCPs in terms of Riemann-Liouville Fractional Derivatives (RLFDs). It is demonstrated that right RLFDs automatically arise in the formulation even when the dynamics of the system is described using left RLFDs only. For numerical computation, the FDs are approximated using the Grunwald-Letnikov definition. This leads to a set of algebraic equations that can be solved using numerical techniques. Two examples, one time-invariant and the other time-variant, are considered to demonstrate the effectiveness of the formulation. Results show that as the order of the derivative approaches an integer value, these formulations lead to solutions for integer order system. The approach requires dividing of the entire time domain into several sub-domains. Further, as the sizes of the sub-domains are reduced, the solutions converge to unique solutions. However, the convergence is slow. A scheme that improves the convergence rate will be considered in a future paper. Other issues to be considered in the future include formulations using other types of derivatives, nonlinear and stochastic fractional optimal controls, existence and uniqueness of the solutions, and the error analysis.
A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges
(Elsevier Science Bv, 2011) Umul, Yusuf Ziya; Umul, Yusuf Ziya; 42699
The solution of Maliuzhinets of the diffraction problem of waves by an impedance wedge is transformed into a physical optics integral. The resultant expression is suitable for the investigation of various diffraction problems having impedance wedges. The method is applied to the scattering of waves by an impedance spherical reflector with wedge structure at its discontinuity. The results are examined numerically. (C) 2011 Elsevier B.V. All rights reserved.
A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations
(Hindawi Ltd, 2013) Doha, E. H.; Baleanu, Dumitru; Baleanu, D.; Bhrawy, A. H.; Abdelkawy, M. A.; 56389
We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters alpha and beta In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.
A k-Dimensional System of Fractional Finite Difference Equations
(Hindawi Ltd, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389
We 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.
A k-Dimensional System of Fractional Neutral Functional Differential Equations with Bounded Delay
(Hindawi Ltd, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389
In 2010, Agarwal et al. studied the existence of a one-dimensional fractional neutral functional differential equation. In this paper, we study an initial value problem for a class of k-dimensional systems of fractional neutral functional differential equations by using Krasnoselskii's fixed point theorem. In fact, our main result generalizes their main result in a sense..
A Local Fractional Variational Iteration Method for Laplace Equation Within Local Fractional Operators
(Hindawi Ltd, 2013) Yang, Yong-Ju; Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.
A Maid Came Free: From Sighting to Citing in Tracy Chevalier’s Girl with a Pearl Earring
(Routledge Journals, Taylor & Francis Ltd, 2018) Uzundemir, Ozlem; Uzundemir, Özlem; 49324
Tracy Chevalier's ekphrastic novel Girl with a Pearl Earring explores the relationship between literature and art, as it narrates Jan Vermeer's paintings from the perspective of the story's narrator, Griet, who works as a maid in the Vermeers's house. In her fictional account, Griet gradually becomes the painter's assistant as well as his model, and subverts the gender issues in ekphrasis; the silent and gazed-upon female image in the eponymous painting gains a voice to critique Vermeer's art. This article will deal with Griet's transformation from a young maid into an art critic with respect to the issues in painting, namely colour, light and realistic representation, as well as the paragone between the viewing subject and the viewed object in ekphrasis.
A Mash-Up Application Utilizing Hybridized Filtering Techniques for Recommending Events At A Social Networking Site
(Springer Wien, 2011) Kayaalp, Mehmet; Ozyer, Tansel; Ozyer, Sibel T.; 18980
Event recommendation is one way of gathering people having same likes/dislikes. In today's world, many mass amounts of events are organized at different locations and times. Generally, cliques of people are fans of some specific events. They attend together based on each other's recommendation. Generally, there are many activities that people prefer/opt out attending and these events are announced for attracting relevant people. Rather than, peerto-peer oracles of a local group of people, or sentiments of people from different sources, an intelligent recommendation system can be used at a social networking site in order to recommend people in collaborative and content basis within a social networking site. We have used an existing social environment (http://www.facebook.com) for deployment. Our application has also been integrated with several web sites for collecting information for assessment. Our system has been designed in modules so that it is open to new data sources either by using web services or web scraping. Currently, our application is yet an application that permits users rate events; they have attended or have beliefs on them. Given the social network between people, system tries to recommend upcoming events to users. For this purpose, we have exploited the fact that a similarity relationship between different events can exist in terms of both content and collaborative filtering. Geographical locations have an impact so; we have also taken geographical location information and social concept of an event. Eventually, our system integrates different sources in facebook (http://www.facebook.com) for doing recommendation between people in close relationship. We have performed experiments among a group of students. Experiments led us have promising results.
A Mechanical Model Based on Conformal Strain Energy and Its Application to Bending and Buckling of Nanobeam Structures
(Asme, 2019) Rahimi, Zaher; Baleanu, Dumitru; Sumelka, Wojciech; Baleanu, Dumitru; 56389
In the present work, a nonlocal model based on the conformal strain energy, utilizing the conformable derivative definition, has been obtained. The model has two additional free parameters compared to the classical (local) mechanical formulations. The first one specifies the amount of the integer and the noninteger gradient of strain in the strain energy relation, and the second one controls the order of the strain derivatives in the conformable energy relation. The obtained governing (nonlinear) equation has been solved by the Galerkin method and the effects of both free parameters have been shown. As a case study, the bending and buckling of nanobeam structures has been studied.
A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line
(Hindawi Ltd, 2014) Bhrawy, Ali H.; Baleanu, Dumitru; AlZahrani, Abdulrahim; Baleanu, Dumitru; Alhamed, Yahia; 56389
The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
A Nagumo-like uniqueness theorem for fractional differential equations
(Iop Publishing Ltd, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal
We extend to fractional differential equations a recent generalization of the Nagumo uniqueness theorem for ordinary differential equations of first order.
A New Analysis of the Fornberg-Whitham Equation Pertaining to A Fractional Derivative With Mittag-Leffler-Type Kernel
(Springer Heidelberg, 2018) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; 56389
The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.
A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence
(Amer inst Physics, 2019) Jajarmi, Amin; Baleanu, Dumitru; Ghanbari, Behzad; Baleanu, Dumitru; 56389
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.
A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications
(Mdpi, 2019) Ghaffar, Abdul; Baleanu, Dumitru; Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.
A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach
(Frontiers Media Sa, 2019) Jajarmi, Amin; Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Asad, Jihad H.; 56389
In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler-Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler-Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag-Leffler non-singular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modeling. Finally, we report our numerical findings to verify the theoretical analysis.

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