Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - WoS: 14
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.
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.
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: 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.

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