Browsing by Author "Defterli, Özlem"

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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 - Scopus: 1
A Fractional Lagrangian Approach for Two Masses with Linear and Cubic Nonlinear Stiffness
(Institute of Electrical and Electronics Engineers Inc., 2023) Defterli, O.; Defterli, Özlem; Baleanu, D.; Jajarmi, A.; Wannan, R.; Asad, J.; 31401; 56389; Matematik
In this manuscript, the fractional dynamics of the two-mass spring system with two kinds of stiffness, namely linear and strongly nonlinear, are investigated. The corresponding fractional Euler-Lagrange equations of the system are derived being a system of two-coupled fractional differential equations with strong cubic nonlinear term. The numerical results of the system are obtained using Euler's approximation method and simulated with respect to the different values of the model parameters as mass, stiffness and order of the fractional derivative in use. The interpretation of the approximate results of the so-called generalized two-mass spring system is discussed via the fractional order. © 2023 IEEE.
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.
About Some New Developments in Fractional Variational Principles
(10th International Conference on Non-Integer Calculus and Its Applications (RRNR2018), 2018) Defterli, Özlem; 31401; Matematik
Citation - Scopus: 1
Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks
(Springer New York LLC, 2014) Defterli, Ö.; Defterli, Özlem; Purutçuoğlu, V.; Weber, G.-W.; 31401; Matematik
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.
Corrigendum to A Numerical Scheme for Two Dimensional Optimal Control Problems With Memory Effect
(2010) Defterli, Özlem; 31401; Matematik
Citation - Scopus: 87
Fractional diffusion on bounded domains
(Walter de Gruyter GmbH, 2015) Defterli, O.; Defterli, Özlem; D'Elia, M.; Du, Q.; Gunzburger, M.; Lehoucq, R.; Meerschaert, M.M.; Matematik
The mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. This paper discusses the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains. © 2015 Diogenes Co., Sofia.
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: 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.
Hidden symmetries of two dimensional superintegrable systems
(2007) Defterli, Özlem; Baleanu, Dumitru; 56389; 31401; Matematik
Classification of the invariants of two - dimensional superintegrable systems is presented. The hidden symmetries associated to the existence of Killing - Yano tensors are investigated.
Infectious Disease Dynamics within Advanced Fractional Operators
(2019) Defterli, Özlem; Arshad, Sadia; Jajarmi, Amin; 31401; Matematik
Citation - WoS: 5
Citation - Scopus: 4
Killing-Yano tensors and angular momentum
(inst Physics Acad Sci Czech Republic, 2004) Baleanu, Dumitru; Baleanu, D; Defterli, Z; Defterli, Özlem; 56389; 31401; Matematik
New geometries were obtained by adding a suitable term involving the components of the angular momentum to the corresponding free Lagrangians. Killing vectors, Killing-Yano and Killing tensors of the obtained manifolds were investigated.
Citation - WoS: 1
Citation - Scopus: 1
Killing-Yano tensors and superintegrable systems
(inst Physics Acad Sci Czech Republic, 2004) Defterli, Özlem; Defterli, Ö; Baleanu, D; Baleanu, Dumitru; 31401; 56389; Matematik
Killing-Yano (KY) and Killing tensors of the four types of metrics, that represent the two-dimensional spaces given in Darboux's classification, are obtained. It is proved that all spaces admit dual manifolds and their KY tensors are calculated.
Citation - WoS: 0
Killing-Yano tensors, surface terms and superintegrable systems
(Amer inst Physics, 2004) Baleanu, Dumitru; Baleanu, D; Defterli, Ö; Defterli, Özlem; 56389; 31401; Matematik
Killing-Yano and Killing tensors are investigated corresponding to a set of two dimensional superintegrable systems. A suitable surface term is added to the corresponding free Lagrangian describing the motion of a particle on a 2-sphere of unit radius and we analyze the symmetries of the obtained geometries.
Mathematical aspects of superintgrable systems
(2004) Defterli, Özlem; Matematik
Superintegrallenebilir Sistemler