Browsing by Author "Defterli, Ozlem"

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Citation - WoS: 165
A central difference numerical scheme for fractional optimal control problems
(Sage Publications Ltd, 2009) Baleanu, Dumitru; Baleanu, Dumitru; Defterli, Ozlem; Defterli, Özlem; Agrawal, Om P.; 56389; 31401; Matematik
This paper presents a modified numerical scheme for a class of fractional optimal control problems where a fractional derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire time domain is divided into several sub-domains, and a FD at a time node point is approximated using a modified Grunwald-Letnikov approach. For the first-order derivative, the proposed modified Grunwald-Letnikov definition leads to a central difference scheme. When the approximations are substituted into the fractional optimal control equations, it leads to a set of algebraic equations which are solved using a direct numerical technique. Two examples, one time-invariant and the other time-variant, are considered to study the performance of the numerical scheme. Results show that 1) as the order of the derivative approaches an integer value, these formulations lead to solutions for the integer-order system, and 2) as the sizes of the sub-domains are reduced, the solutions converge. It is hoped that the present scheme would lead to stable numerical methods for fractional differential equations and optimal control problems.
Citation - WoS: 8
Citation - Scopus: 8
A novel fractional grey model applied to the environmental assessment in Turkey
(World Scientific Publ Co Pte Ltd, 2020) Defterli, Özlem; Shaheen, Aliya; Sheng, Jinyong; Baleanu, Dumitru; Arshad, Sadia; Defterli, Ozlem; Xie, Xiaoqing; Baleanu, Dumitru; 31401; 56389; Matematik
This study presents a novel fractional order grey model FGM (alpha,1) obtained by extending the grey model (GM (1,1)). For this, we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of order alpha. A real-world case study, scrutinize the economic growth influence on environmental degradation in Turkey, is performed to evaluate the significance of the projected model FGM (alpha,1) in contrast to the current classical GM. We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and short-run relation among economic growth, agriculture, forestry and fishing (AFF), electricity utilization and CO2 emissions. Using the new fractional order model, all the variables are forecasted in the forthcoming years until 2030. Findings disclose that electricity utilization and economic growth (GDP) accelerate emission of CO2 though in the long run agriculture, forestry, and fishing reduce the environmental pollution in Turkey.
Citation - WoS: 7
Citation - Scopus: 7
A numerical framework for the approximate solution of fractional tumor-obesity model
(World Scientific Publ Co Pte Ltd, 2019) Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; Defterli, Özlem; Defterli, Ozlem; Shumaila; 56389; Matematik
In this paper, we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and Caputo-Fabrizio (CF). Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed. Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models. We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.
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; Defterli, Özlem; 31401; Matematik
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.
Citation - WoS: 39
Citation - Scopus: 41
A Second Order Accurate Approximation for Fractional Derivatives With Singular and Non-Singular Kernel Applied to A Hıv Model
(Elsevier Science inc, 2020) Defterli, Özlem; Arshad, Sadia; Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
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.
Citation - WoS: 12
Citation - Scopus: 13
Comparative analysis of fractional order dengue model with temperature effect via singular and non-singular operators
(Pergamon-elsevier Science Ltd, 2021) Defterli, Ozlem; Defterli, Özlem; 31401; Matematik
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.
Citation - WoS: 6
Citation - Scopus: 7
Fractional investigation of time-dependent mass pendulum
(Sage Publications Ltd, 2024) Baleanu, Dumitru; Baleanu, Dumitru; Jajarmi, Amin; Defterli, Özlem; Defterli, Ozlem; Wannan, Rania; Sajjadi, Samaneh S.; Asad, Jihad H.; 56389; 31401; Matematik
In this paper, we aim to study the dynamical behaviour of the motion for a simple pendulum with a mass decreasing exponentially in time. To examine this interesting system, we firstly obtain the classical Lagrangian and the Euler-Lagrange equation of the motion accordingly. Later, the generalized Lagrangian is constructed via non-integer order derivative operators. The corresponding non-integer Euler-Lagrange equation is derived, and the calculated approximate results are simulated with respect to different non-integer orders. Simulation results show that the motion of the pendulum with time-dependent mass exhibits interesting dynamical behaviours, such as oscillatory and non-oscillatory motions, and the nature of the motion depends on the order of non-integer derivative; they also demonstrate that utilizing the fractional Lagrangian approach yields a model that is both valid and flexible, displaying various properties of the physical system under investigation. This approach provides a significant advantage in understanding complex phenomena, which cannot be achieved through classical Lagrangian methods. Indeed, the system characteristics, such as overshoot, settling time, and peak time, vary in the fractional case by changing the value of & alpha;. Also, the classical formulation is recovered by the corresponding fractional model when & alpha; tends to 1, while their output specifications are completely different. These successful achievements demonstrate diverse properties of physical systems, enhancing the adaptability and effectiveness of the proposed scheme for modelling complex dynamics.
Citation - WoS: 104
Citation - Scopus: 129
Fractional optimal control problems with several state and control variables
(Sage Publications Ltd, 2010) Defterli, Özlem; Agrawal, Om P.; Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; 31401; Matematik
In many applications, fractional derivatives provide better descriptions of the behavior of dynamic systems than other techniques. For this reason, fractional calculus has been used to analyze systems having noninteger order dynamics and to solve fractional optimal control problems. In this study, we describe a formulation for fractional optimal control problems defined in multi-dimensions. We consider the case where the dimensions of the state and control variables are different from each other. Riemann-Liouville fractional derivatives are used to formulate the problem. The fractional differential equations involving the state and control variables are solved using Grunwald-Letnikov approximation. The performance of the formulation is shown using an example.
Citation - WoS: 90
Citation - Scopus: 105
Fractional Treatment: An Accelerated Mass-Spring System
(Editura Acad Romane, 2022) Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H.; 56389; 31401; Matematik
The aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and derive the classical equations of motion using the Euler-Lagrange equations of integer-order. Furthermore, the generalized Lagrangian is introduced by using non-integer, so-called fractional, derivative operators; then the resulting fractional Euler-Lagrange equations are generated and solved numerically. The obtained results are presented illustratively by using numerical simulations.
Citation - WoS: 49
Citation - Scopus: 51
Fuzzy prediction strategies for gene-environment networks - fuzzy regression analysis for two-modal regulatory systems
(Edp Sciences S A, 2016) Kropat, Erik; Defterli, Özlem; Ozmen, Ayse; Weber, Gerhard-Wilhelm; Meyer-Nieberg, Silja; Defterli, Ozlem; 31401; Matematik
Target-environment networks provide a conceptual framework for the analysis and prediction of complex regulatory systems such as genetic networks, eco-finance networks or sensor-target assignments. These evolving networks consist of two major groups of entities that are interacting by unknown relationships. The structure and dynamics of the hidden regulatory system have to be revealed from uncertain measurement data. In this paper, the concept of fuzzy target-environment networks is introduced and various fuzzy possibilistic regression models are presented. The relation between the targets and/or environmental entities of the regulatory network is given in terms of a fuzzy model. The vagueness of the regulatory system results from the (unknown) fuzzy coefficients. For an identification of the fuzzy coefficients' shape, methods from fuzzy regression are adapted and made applicable to the bi-level situation of target-environment networks and uncertain data. Various shapes of fuzzy coefficients are considered and the control of outliers is discussed. A first numerical example is presented for purposes of illustration. The paper ends with a conclusion and an outlook to future studies.
Citation - WoS: 11
Citation - Scopus: 14
Modeling the impact of temperature on fractional order dengue model with vertical transmission
(Ramazan Yaman, 2020) Defterli, Ozlem; Defterli, Özlem; 31401; Matematik
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.
Citation - WoS: 50
Citation - Scopus: 58
Modeling, inference and optimization of regulatory networks based on time series data
(Elsevier, 2011) Weber, Gerhard-Wilhelm; Defterli, Özlem; Defterli, Ozlem; Gok, Sirma Zeynep Alparslan; Kropat, Erik; ; 31401; 107899; Matematik
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.
Citation - WoS: 8
Citation - Scopus: 8
Modern tools for the time-discrete dynamics and optimization of gene-environment networks
(Elsevier, 2011) Defterli, Ozlem; Defterli, Özlem; Fuegenschuh, Armin; Weber, Gerhard Wilhelm; 31401; Matematik
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.
Citation - WoS: 0
Citation - Scopus: 0
A Numerical Scheme for Two Dimensional Optimal Control Problems With Memory Effect (Vol 59, Pg 1630, 2010)
(Pergamon-elsevier Science Ltd, 2010) Defterli, Ozlem
Citation - WoS: 96
Citation - Scopus: 107
On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control
(Springer, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; 56389; Matematik
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.
Citation - WoS: 1
Citation - Scopus: 1
On Generalized Asymmetric Harmonic Oscillator With Quadratic Nonlinearity Within Fractional Variational Principles
(Sage Publications Ltd, 2024) Baleanu, Dumitru; Jajarmi, Amin; Defterli, Ozlem; Mohammad, Noorhan F. AlShaikh; Asad, Jihad; Matematik
This work studies the nonlinear fractional dynamics of asymmetric harmonic oscillators. The classical description of the physical system is generalized using the principles of fractional variational analysis. As a system of two-coupled fractional differential equations with a quadratic nonlinear component, the fractional Euler-Lagrange equations of the motion of the corresponding system are obtained. The Adams-Bashforth predictor-corrector numerical approach is used to approximate the system's outcomes, which are then simulated comparatively with respect to various model parameter values, including mass, linear and quadratic nonlinear stiffness, and the order of the fractional derivative. The simulations provided the possibility of investigating various dynamical behaviours within the same physical model that is generalized by the use of fractional operators.
Citation - WoS: 3
Citation - Scopus: 5
Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model
(Iop Publishing Ltd, 2021) Defterli, Özlem; Arshad, Sadia; Saleem, Iram; Baleanu, Dumitru; Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; 56389; Matematik
This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.
Citation - WoS: 0
Citation - Scopus: 0
Symplectic algorithm for systems with second-class constraints
(inst Physics Acad Sci Czech Republic, 2006) Defterli, Özlem; Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; 31401; Matematik
The recently modified Faddeev-Jackiw formalism for systems having one chain of four levels of only second-class constraints is applied to the non-trivial a = 1 bosonized chiral Schwinger model in (1+1) dimensions as well as to one mechanical system. The sets of obtained constraints are in agreement with Dirac's canonical formulation.
Citation - WoS: 82
Citation - Scopus: 94
The fractional dynamics of a linear triatomic molecule
(Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; 56389; Matematik
In this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.
Citation - WoS: 30
Citation - Scopus: 35
The new robust conic GPLM method with an application to finance: prediction of credit default
(Springer, 2013) Ozmen, Ayse; Defterli, Özlem; Weber, Gerhard-Wilhelm; Cavusoglu, Zehra; Defterli, Ozlem; 31401; Matematik
This paper contributes to classification and identification in modern finance through advanced optimization. In the last few decades, financial misalignments and, thereby, financial crises have been increasing in numbers due to the rearrangement of the financial world. In this study, as one of the most remarkable of these, countries' debt crises, which result from illiquidity, are tried to predict with some macroeconomic variables. The methodology consists of a combination of two predictive regression models, logistic regression and robust conic multivariate adaptive regression splines (RCMARS), as linear and nonlinear parts of a generalized partial linear model. RCMARS has an advantage of coping with the noise in both input and output data and of obtaining more consistent optimization results than CMARS. An advanced version of conic generalized partial linear model which includes robustification of the data set is introduced: robust conic generalized partial linear model (RCGPLM). This new model is applied on a data set that belongs to 45 emerging markets with 1,019 observations between the years 1980 and 2005.