Akademik Çıktılar

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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 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 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 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 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 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.
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
(Amer inst Physics, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; 56389
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.
A New Neumann Series Method for Solving A Family of Local Fractional Fredholm and Volterra Integral Equations
(Hindawi Ltd, 2013) Ma, Xiao-Jing; Baleanu, Dumitru; Srivastava, H. M.; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.
A new representation of the Kirchhoffs diffraction integral
(Elsevier Science Bv, 2013) Umul, Yusuf Ziya; Umul, Yusuf Ziya; 42699
The diffraction integral of Kirchhoff is rearranged according to its integral boundaries. The new approach is based on the theory of the edge dislocation waves and provides a more correct field representation for the semi-infinite and infinite integrals in the direct numerical computation. The integral is studied on the diffraction problem of plane waves by a perfectly conducting half-plane. The correctness of the scattering diagrams is compared with the classical approach and the Fresnel integral representation of the scattered waves numerically. (c) 2012 Elsevier B.V. All rights reserved.
A novel numerical approach for a nonlinear fractional dynamical model of interpersonal and romantic relationships
(Mdpi, 2017) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian's decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter h and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
A Novel Technique to Construct Exact Solutions for Nonlinear Partial Differential Equations
(Springer Heidelberg, 2019) Ghanbari, Behzad; Baleanu, Dumitru; Baleanu, Dumitru; 56389
The aim of the manuscript is to present a new exact solver of nonlinear partial differential equations. The proposed technique is developed by extending the phi(6)-model expansion method as a known method. The corresponding exact solutions are given in terms of Jacobi elliptic functions. Some new optical solutions of the resonant nonlinear Schrodinger equation are constructed within this newly proposed method. For some specific choices of the modulus of Jacobi elliptic functions, various solutions of the equation are introduced. Some numerical simulations are also included to emphasize that all parameters have major influences for the solitary waves behaviours. The proposed technique is very simple and straightforward, and can be employed to solve other non-linear partial differential equations.
A phenomenological study on ferroelectric pyridinium tetrafluoroborate (C5NH6) BF4
(Elsevier, 2019) Kiraci, A.; Kiracı, Ali; 42475
The temperature dependence of the specific heat C-V of (C5NH6)BF4 was analyzed according to a power law formula with a critical exponent alpha deduced from the compressible Ising model in the vicinity of the phase transition temperatures of T-C1 = 238 K and T-C2 = 204 K. The extracted values of the critical exponent alpha within the temperature intervals of vertical bar T - T-C1 vertical bar < 6 K and also T - T-C2 < 6 K were consistent with that predicted from the 3d-Ising model (alpha = 0.10) while obtained values of alpha within the temperature interval of T-C2 - T < 6 K were consistent with that predicted from 2-d potts model (alpha = 0.30). In addition, the thermodynamic quantities: the internal energy (U), the entropy (S) and the Helmholtz free energy (F) of this compound were calculated on the basis of the extracted values of the critical exponent a below and above the phase transition temperatures of T-C1 and T-C2.
A Unique Coupled Common Fixed Point Theorem for Symmetric (P,P) -Contractive Mappings in Ordered G -Metric Spaces With Applications
(Hindawi Ltd, 2013) Jain, Manish; Taş, Kenan; Tas, Kenan; 4971
We establish the existence and uniqueness of coupled common fixed point for symmetric (phi, psi)-contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011), Nashine (2012), and Mohiuddine and Alotaibi (2012), thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.
A zero-crossing technique for the multidetermination of thiamine HCl and pyridoxine HCl in their mixture by using one-dimensional wavelet transform
(Elsevier, 2003) Dinç, E; Baleanu, Dumitru; Baleanu, D; 56389
A new zero-crossing technique based on one-dimensional wavelet transform (WT) was developed and applied on a commercial vitamin product and binary mixtures containing thiamine HCl and pyridoxine HCl in the presence of the interference of the analysed signals. We selected from the data of the UV-Vis absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg/ml for both vitamins and we subjected it to one-dimensional continuous WT Mexican (MEXICAN) and Meyer (MEYER). Since the peaks of the transformed signals were bigger than original ones a zero crossing technique was applied to obtain the regression equations. The validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. The basic concepts about wavelet method were briefly explained and MATLAB 6.5 software was used for one-dimensional wavelet analysis, The obtained results were successfully compared among each other and with those obtained by other literature methods. The developed method is rapid, easy to apply. not expensive and suitable for analysing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment. (C) 2003 Elsevier Science B.V. All rights reserved.

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