Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 75Citation - Scopus: 82Mathematical Modeling of Pine Wilt Disease With Caputo Fractional Operator(Pergamon-elsevier Science Ltd, 2021) Acay, Bahar; Mustapha, Umar Tasiu; Inc, Mustafa; Baleanu, Dumitru; Yusuf, AbdullahiIn this work, we investigate the transmission dynamics of pine wilt disease infection and developed a new model utilizing Caputo fractional-order derivative. Moreover, with the use of fixed point theorem, the existence and uniqueness of the pine wilt disease model are obtained under Caputo operator. Using forward normalized sensitivity index, we determine the most sensitive parameters essential for the control of the infection and the results show that, decreasing the values of contact rate of a susceptible vector with infected pine trees and progression rate play a significant role in controlling the spread of pine wilt disease infection. On the other hand, we obtain different numerical simulations results of the model using the appropriate parameter values. Hence, from the graphs, it can be concluded that Caputo fractional operator gives more biologically observable behavior of the proposed disease model thanks to the changed fractional order. Compared to the previously built integer order model, the non-integer order derivative provided more efficient and flexible information about the complexity of the model's dynamics. (c) 2020 Elsevier Ltd. All rights reserved.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: 35Citation - Scopus: 38Efficiency of the New Fractional Derivative With Nonsingular Mittag-Leffler Kernel To Some Nonlinear Partial Differential Equations(Pergamon-elsevier Science Ltd, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi; Isa Aliyu, AliyuIn this work, the efficiency of the Atangana-Baleanu (AB) derivative over Caputo-Fabrizio (CF) to some nonlinear partial differential equation is presented. The considered equations are Rosenou-Haynam equation (RHE) and a class of mKdV (CmKdV) equation. The effective and efficient technique called the fractional homotopy perturbation transform method (FHPTM) is applied for the investigation of the governing equations. (C) 2018 Elsevier Ltd. All rights reserved.