Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 81Citation - Scopus: 94The 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.; MatematikIn 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.Article Citation - WoS: 104Citation - Scopus: 119Fractional Treatment: an Accelerated Mass-Spring System(Editura Acad Romane, 2022) Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; Defterli, Özlem; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H.; MatematikThe 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.Article Citation - WoS: 3Citation - Scopus: 5Simpson's Method for Fractional Differential Equations With a Non-Singular Kernel Applied To a Chaotic Tumor Model(Iop Publishing Ltd, 2021) Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; Arshad, Sadia; Saleem, IramThis 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.Article Citation - WoS: 15Citation - Scopus: 14Comparative Analysis of Fractional Order Dengue Model With Temperature Effect Via Singular and Non-Singular Operators(Pergamon-elsevier Science Ltd, 2021) Defterli, OzlemIn 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: 8Citation - Scopus: 8A Novel Fractional Grey Model Applied To the Environmental Assessment in Turkey(World Scientific Publ Co Pte Ltd, 2020) Arshad, Sadia; Defterli, Ozlem; Xie, Xiaoqing; Baleanu, Dumitru; Shaheen, Aliya; Sheng, JinyongThis 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.Article Citation - WoS: 39Citation - Scopus: 42A 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, OzlemIn 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: 138Citation - Scopus: 147Thermal 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, RizwanThe 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: 7Citation - Scopus: 7A Numerical Framework for the Approximate Solution of Fractional Tumor-Obesity Model(World Scientific Publ Co Pte Ltd, 2019) Defterli, Ozlem; Shumaila; Arshad, Sadia; Baleanu, DumitruIn 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.Article Citation - WoS: 30Citation - Scopus: 36The New Robust Conic Gplm Method With an Application To Finance: Prediction of Credit Default(Springer, 2013) Weber, Gerhard-Wilhelm; Cavusoglu, Zehra; Defterli, Ozlem; Ozmen, AyseThis 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.Article Citation - WoS: 8Citation - Scopus: 8Modern Tools for the Time-Discrete Dynamics and Optimization of Gene-Environment Networks(Elsevier, 2011) Fuegenschuh, Armin; Weber, Gerhard Wilhelm; Defterli, Ozlem; Fügenschuh, ArminIn 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.