WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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20202

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  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    An Algebraic Stability Test for Fractional Order Time Delay Systems
    (Ramazan Yaman, 2020) Baleanu, Dumitru; Ozyetkin, Munevver Mine
    In this study, an algebraic stability test procedure is presented for fractionalorder time delay systems. This method is based on the principle of eliminatingtime delay. The stability test of fractional order systems cannot be examineddirectly using classical methods such as Routh-Hurwitz, because such systemsdo not have analytical solutions. When a system contains the square roots ofs, it is seen that there is a double value function of s. In this study, a stabilitytest procedure is applied to systems including ps and/or different fractionaldegrees such as s where 0 < α < 1, and αǫR. For this purpose, the integerorder equivalents of fractional order terms are first used and then the stabilitytest is applied to the system by eliminating time delay. Thanks to the proposedmethod , it is not necessary to use approximations instead of time delay termsuch as Pad´e. Thus, the stability test procedure does not require the solutionof higher order equations.
  • Article
    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.