Matematik Bölümü Yayın Koleksiyonu

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Author: search.filters.author.Defterli, OzlemWoS Q: search.filters.wosQuartile.Q1

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  • Article
    Citation - WoS: 101
    Citation - Scopus: 115
    On a Nonlinear Dynamical System With Both Chaotic and Nonchaotic Behaviors: a New Fractional Analysis and Control
    (Springer, 2021) Jajarmi, Amin; Defterli, Ozlem; Baleanu, Dumitru; Sajjadi, Samaneh Sadat
    In this paper, we aim to analyze the complicated dynamical motion of a quarter-car suspension system with a sinusoidal road excitation force. First, we consider a new mathematical model in the form of fractional-order differential equations. In the proposed model, we apply the Caputo-Fabrizio fractional operator with exponential kernel. Then to solve the related equations, we suggest a quadratic numerical method and prove its stability and convergence. A deep investigation in the framework of time-domain response and phase-portrait shows that both the chaotic and nonchaotic behaviors of the considered system can be identified by the fractional-order mathematical model. Finally, we present a state-feedback controller and a chaos optimal control to overcome the system chaotic oscillations. Simulation results demonstrate the effectiveness of the proposed modeling and control strategies.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 14
    Comparative Analysis of Fractional Order Dengue Model With Temperature Effect Via Singular and Non-Singular Operators
    (Pergamon-elsevier Science Ltd, 2021) Defterli, Ozlem
    In this work, we generalize a (deterministic) mathematical model that anticipates the influence of temperature on dengue transmission incorporating temperature-dependent model parameters. The motivation comes by the epidemiological evidence and several recent studies clearly states fluctuations in temperature, rainfall, and global climate indexes are determinant on the transmission dynamic and epidemic behavior of dengue virus that causes deadly diseases with incidence rates significantly risen worldwide in the past decade. Taking into account the importance of the subject in nowadays and the diversity of fractional calculus operators in mathematical modeling of complex real-world systems, in this paper we investigated the importance of the new model based on Mittag-Leffler kernel as being non-singular kernel. The sensitivity analysis of the generalized model is newly investigated. Numerical simulations are carried out in a comparative sense within the temperature fluctuations for both singular and non-singular fractional operators of different orders. (c) 2021 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 16
    Modeling the Impact of Temperature on Fractional Order Dengue Model With Vertical Transmission
    (Ramazan Yaman, 2020) Defterli, Ozlem
    A dengue epidemic model with fractional order derivative is formulated to an-alyze the effect of temperature on the spread of the vector-host transmitted dengue disease. The model is composed of a system of fractional order differ-ential equations formulated within Caputo fractional operator. The stability of the equilibrium points of the considered dengue model is studied. The cor-responding basic reproduction number R alpha 0 is derived and it is proved that if R alpha 0 < 1, the disease-free equilibrium (DFE) is locally asymptotically stable. L1 method is applied to solve the dengue model numerically. Finally, numerical simulations are also presented to illustrate the analytical results showing the influence of the temperature on the dynamics of the vector-host interaction in dengue epidemics.
  • Article
    Citation - WoS: 39
    Citation - Scopus: 42
    A Second Order Accurate Approximation for Fractional Derivatives With Singular and Non-Singular Kernel Applied To a Hiv Model
    (Elsevier Science inc, 2020) Baleanu, Dumitru; Arshad, Sadia; Defterli, Ozlem
    In this manuscript we examine the CD4(+) T cells model of HIV infection under the consideration of two different fractional differentiation operators namely Caputo and Caputo-Fabrizio (CF). Moreover, the generalized HIV model is investigated by considering Reverse Transcriptase (RT) inhibitors as a drug treatment for HIV. The threshold values for the stability of the equilibrium point belonging to non-infected case are calculated for both models with and without treatment. For the numerical solutions of the studied model, we construct trapezoidal approximation schemes having second order accuracy for the approximation of fractional operators with singular and non-singular kernel. The stability and convergence of the proposed schemes are analyzed analytically. To illustrate the dynamics given by these two fractional operators, we perform numerical simulations of the HIV model for different biological scenarios with and without drug concentration. The studied biological cases are identified by considering different values of the parameters such as infection rate, growth rate of CD4(+) T cells, clearance rate of virus particles and also the order of the fractional derivative. (C) 2020 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 138
    Citation - Scopus: 147
    Thermal and Velocity Slip Effects on Casson Nanofluid Flow Over an Inclined Permeable Stretching Cylinder Via Collocation Method
    (Pergamon-elsevier Science Ltd, 2018) Soomro, Feroz Ahmed; Haq, Rizwan Ul; Wang, W.; Defterli, Ozlem; Usman, M.; Ul Haq, Rizwan
    The main emphasis of present work is to investigate the velocity and thermal slip effects on Casson nano fluid with heat and mass transfer phenomena over an inclined permeable stretching cylinder. The cylinder is subject to transverse magnetic field. Buongiorno's model is adapted to study the Brownian motion and thermphoresis effects which play a dominant role in nanofluid. Governing set of equations are derived in terms of partial differential equations for Casson nanofluid model, consisting continuity, momentum, energy and concentration equation which are transformed into set of coupled nonlinear ordinary differential equations using similarity transformation. The numerical solution is obtained using collocation method. The literature survey shows that the present problem has not been studied before. Physical quantities of interest are nanofluid velocity, temperature, concentration, skin friction coefficient, Nusselt number and Sherwood number which are analyzed through graphs against the emerging physical parameters. It is found that Nb and Nt play a dominant role within the thermal and concentration boundary layer regions. In the same manner, suction parameter and both velocity and thermal slip parameters depicts the dynamic effects in the entire domain of stretching surface of the cylinder. (C) 2018 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Modern Tools for the Time-Discrete Dynamics and Optimization of Gene-Environment Networks
    (Elsevier, 2011) Fuegenschuh, Armin; Weber, Gerhard Wilhelm; Defterli, Ozlem; Fügenschuh, Armin
    In this study, we discuss the models of genetic regulatory systems, so-called gene-environment networks. The dynamics of such kind of systems are described by a class of time-continuous ordinary differential equations having a general form (E) over dot = M(E)E, where E is a vector of gene-expression levels and environmental factors and M(E) is the matrix having functional entries containing unknown parameters to be optimized. Accordingly, time-discrete versions of that model class are studied and improved by introducing 3rd-order Heun's method and 4th-order classical Runge-Kutta method. The corresponding iteration formulas are derived and their matrix algebras are obtained. After that, we use nonlinear mixed-integer programming for the parameter estimation in the considered model and present the solution of a constrained and regularized given mixed-integer problem as an example. By using this solution and applying both the new and existing discretization schemes, we generate corresponding time-series of gene-expressions for each method. The comparison of the experimental data and the calculated approximate results is additionally done with the help of the figures to exercise the performance of the numerical schemes on this example. (C) 2011 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 54
    Citation - Scopus: 63
    Modeling, Inference and Optimization of Regulatory Networks Based on Time Series Data
    (Elsevier, 2011) Defterli, Ozlem; Gok, Sirma Zeynep Alparslan; Kropat, Erik; Weber, Gerhard-Wilhelm; Alparslan Gök, Sirma Zeynep
    In this survey paper, we present advances achieved during the last years in the development and use of OR, in particular, optimization methods in the new gene-environment and eco-finance networks, based on usually finite data series, with an emphasis on uncertainty in them and in the interactions of the model items. Indeed, our networks represent models in the form of time-continuous and time-discrete dynamics, whose unknown parameters we estimate under constraints on complexity and regularization by various kinds of optimization techniques, ranging from linear, mixed-integer, spline, semi-infinite and robust optimization to conic, e.g., semi-definite programming. We present different kinds of uncertainties and a new time-discretization technique, address aspects of data preprocessing and of stability, related aspects from game theory and financial mathematics, we work out structural frontiers and discuss chances for future research and OR application in our real world. (C) 2010 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 23
    A Numerical Scheme for Two-Dimensional Optimal Control Problems With Memory Effect
    (Pergamon-elsevier Science Ltd, 2010) Defterli, Ozlem
    A new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.