Akademik Çıktılar

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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 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 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 Numerical Techhique For Solving Fractional Partial Differential Equations
(Univ Miskolc inst Math, 2018) Acan, Omer; Baleanu, Dumitru; Baleanu, Dumitru; 56389
We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the same time, conformable reduced differential transform method (CRDTM) for FPDEs is briefly given and a numerical comparison is made between this method and the newly introduced CADM. In applied science, CADM can be used as an alternative method to obtain approximate and analytical solutions for FPDEs as CRDTM. In this study, linear and non-linear three problems are solved by these two methods. In these methods, the obtained solutions take the form of a convergent series with easily computable algorithms. For the applications, the obtained results by these methods are compared to each other and with the exact solutions. When applied to FPDEs, it is seem that CADM approach produces easy, fast and reliable solutions as CRDTM. 2010 Mathematics Subject Classification: 34A08; 34K28
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 Shuffling Technique Based on Fractional Chaotic Maps
(Elsevier Gmbh, 2018) Bai, Yun-Ru; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; 56389
An image encryption technique based on the fractional logistic map is designed in this work. A novel shuffling technique is established by use of fractional chaotic signals. Then it is used to scramble pixel positions. The results are analyzed in comparison with the classical logistic map. Since the employed fractional chaotic map holds complicated dynamics behavior, the encryption result is highly secure. Moreover, by experimental and statistical analysis, we demonstrate that the encryption performance is better than the results in literature. (C) 2018 Published by Elsevier GmbH.
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 practical approach to performance-based building design in architectural project
(Routledge Journals, Taylor & Francis Ltd, 2020) Sayin, Selcuk; Celebi, Gulser
The aim of this study is to develop an approach that can enhance and contribute to the practical applicability of performance-based building design in architectural projects. The need for such an approach is based on the current lack of a practical application for performance-based design in architectural projects, despite the numerous studies conducted in this regard to date. The approach has been applied in a commercial building project designed by an architectural firm in Konya. The performance evaluation of the design developed in accordance with the requirements of the client/builder and the restrictions of regulations was carried out using IES VE 2014 software at a specific phase of the design process. Through this building performance simulation tool; the thermal protection of the envelope/heat loss and solar gain, thermal comfort (temperature, humidity), air quality (freshness), daylight and glare levels were evaluated for the selected spaces in the building, and following the evaluation, new design proposals were put forward to improve the design so as to meet the performance goal.
A robust and accurate disturbance damping control design for nonlinear dynamical systems
(Wiley, 2019) Jajarmi, Amin; Baleanu, Dumitru; Hajipour, Mojtaba; Sajjadi, Samaneh Sadat; Baleanu, Dumitru; 56389
The principle result of this paper is the following disturbance rejection control scheme for a class of nonlinear dynamical systems. By using the internal model principle, the problem of disturbance damping control is converted into a nonlinear quadratic regulator (NQR) problem for an undisturbed augmented system. Then, an iterative technique is designed to solve this NQR problem effectively. The proposed iterative method is also extended through the use of a nonlinear model predictive control in an offline framework. In this case and in the presence of unknown disturbances, the Lyapunov stability of the closed-loop system is guaranteed. Numerical simulations and comparative results verify the effectiveness of the proposed approach.
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.
Adaptive fractional-order blood glucose regulator based on high-order sliding mode observer
(inst Engineering Technology-iet, 2019) Delavari, Hadi; Baleanu, Dumitru; Heydarinejad, Hamid; Baleanu, Dumitru; 56389
Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.
Almost autonomous training of mixtures of principal component analyzers
(Elsevier Science Bv, 2004) Musa, MEM; de Ridder, D; Duin, RPW; Atalay, V
In recent years, a number of mixtures of local PCA models have been proposed. Most of these models require the user to set the number of submodels (local models) in the mixture and the dimensionality of the submodels (i.e., number of PC's) as well. To make the model free of these parameters, we propose a greedy expectation-maximization algorithm to find a suboptimal number of submodels. For a given retained variance ratio, the proposed algorithm estimates for each submodel the dimensionality that retains this given variability ratio. We test the proposed method on two different classification problems: handwritten digit recognition and 2-class ionosphere data classification. The results show that the proposed method has a good performance. (C) 2004 Elsevier B.V. All rights reserved.
Ammonia removal from anaerobically digested dairy manure by struvite precipitation
(Elsevier Sci Ltd, 2005) Uludag-Demirer, S; Demirer, GN; Chen, S
Ammonia is one of the most important contaminants impairing the quality of water resources. When this is considered along with the fact that the global demand for nitrogenous fertilizers is in constant rise, the need for recovery as well as removal of nitrogen is well justified. Crystallization of N and P in the form of struvite (MgNH4PO4 center dot 6H(2)O), which is a slow releasing and valuable fertilizer, is one possible technique for this purpose. This study investigated the removal of NR4+ through struvite precipitation from the effluents of one- (R1) and two-phase (R2) anaerobic reactors digesting dairy manure. To force the formation of struvite in the anaerobic reactor effluents, Ma(2+) ion was added by using both Mg(OH)(2) and MgCl2 center dot 6H(2)O. To prevent the effect of different total phosphorus (TP) concentration in the effluents of RI and R2, as well as to not limit the formation of struvite, an excess amount Of PO43- (0.14 M) was added in the form of NaHPO4. Different stoichiometric Mg2+:NH4+:PO43- ratios were tested to determine the required Mg2+ concentrations for maximum NH4+ removal by keeping NH4+:PO43- ratio constant for the effluents of reactors RI and R2. The results revealed that very high NH4+ removal efficiencies (above 95%) were possible by adding Mg 21 ions higher than 0.06 M concentration in the effluents from reactors RI and R2. It was also observed that the initial pH adjustment to 8.50 using NaOH did not result in any significant increase in the removal of NH4+ and the removal of NH4+ in the reactors treated with MgCl2 center dot 6H(2)O was higher than those treated with Mg(OH)(2) for the same Mg2+ concentration. (c) 2005 Published by Elsevier Ltd.
An analytical solution for the plane wave diffraction by a resistive half-plane residing at the interface of left and right handed media
(Elsevier Gmbh, 2019) Basdemir, Husnu Deniz; Başdemir, Hüsnü Deniz; 20399
The diffraction of waves by a resistive half-plane lying on the interface of left and right handed media is investigated in this study. Because of the anomalous refraction property of left handed media, shadow boundary shifts toward to the lower surface of the half-plane. In order to obtain the shifted boundary, diffracted waves are divided to subfields. Thus, obtained diffracted waves compensates the deficiency of geometries optics fields at the transition regions. The uniform version of waves is obtained by using the uniform theory of diffraction. The wave behaviors are examined numerically.
An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations
(Ieee-inst Electrical Electronics Engineers inc, 2020) Ali, Izaz; Baleanu, Dumitru; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
In the present research article, a modified analytical method is applied to solve time-fractional telegraph equations. The Caputo-operator is used to express the derivative of fractional-order. The present method is the combination of two well-known methods namely Mohan transformation method and Adomian decomposition method. The validity of the proposed technique is confirmed through illustrative examples. It is observed that the obtained solutions have strong contact with the exact solution of the examples. Moreover, it is investigated that the present method has the desired degree of accuracy and provided the graphs closed form solutions of all targeted examples. The graphs have verified the convergence analysis of fractional-order solutions to integer-order solution. In conclusion, the suggested method is simple, straightforward and an effective technique to solve fractional-order partial differential equations.
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
(Mdpi, 2018) Kumar, Devendra; Baleanu, Dumitru; Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; 56389
In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator
(Taylor & Francis Ltd, 2019) Ullah, Malik Zaka; Baleanu, Dumitru; Alzahrani, Abdullah K.; Baleanu, Dumitru; 56389
The present study aims to investigate a new fractional model describing the dynamical behaviour of the tuberculosis infection. In this new formulation, we use a recently introduced fractional operator with Mittag-Leffler nonsingular kernel. To solve and simulate the proposed model, a new and efficient numerical method is developed based on the product-integration rule. Simulation results are provided and some discussions are given to verify the theoretical analysis. The results indicate that employing the nonsingular operator can extract the hidden aspects of the model under consideration while these features are invisible when we use the ordinary time-derivatives. Therefore, the non-integer calculus supplies more flexible models describing the asymptotic behaviours of the real-world phenomena and helps us to better understand their complex dynamics.
An examination of personality traits and how they impact on software development teams
(Elsevier, 2017) Yilmaz, Murat; Yılmaz, Murat; O'Connor, Rory V.; Colomo-Palacios, Ricardo; Clarke, Paul; 55248
Context Research has shown that a significant number of software projects fail due to social issues such as team or personality conflicts. However, only a limited number of empirical studies have been undertaken to understand the impact of individuals' personalities on software team configurations. These studies suffer from an important limitation as they lack a systematic and rigorous method to relate personality traits of software practitioners and software team structures. Objective: Based on an interactive personality profiling approach, the goal of this study is to reveal the personality traits of software practitioners with an aim to explore effective software team structures. Method: To explore the importance of individuals' personalities on software teams, we employed a two-step empirical approach. Firstly, to assess the personality traits of software practitioners, we developed a context-specific survey instrument, which was conducted on 216 participants from a middle-sized soft ware company. Secondly, we propose a novel team personality illustration method to visualize team structures. Results: Study results indicated that effective team structures support teams with higher emotional stability, agreeableness, extroversion, and conscientiousness personality traits. Conclusion: Furthermore, empirical results of the current study show that extroversion trait was more predominant than previously suggested in the literature, which was especially more observable among agile software development teams. (C) 2017 Elsevier B.V. All rights reserved.
Analysis for Fractional-Order Predator–Prey Model With Uncertainty
(inst Engineering Technology-iet, 2019) Narayanamoorthy, Samayan; Baleanu, Dumitru; Baleanu, Dumitru; Thangapandi, Kalidas; Perera, Shyam Sanjeewa Nishantha; 56389
Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.

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