Yazar "Arik, Irem Akbulut" seçeneğine göre listele

Listeleniyor 1 - 4 / 4
  • [ X ]
    Öğe
    Crossover behaviors via piecewise concept: A model of tumor growth and its response to radiotherapy
    (Elsevier, 2022) Arik, Irem Akbulut; Araz, Seda Igret
    This study aims to combine 3 different models, which take into account the pre-treatment, during the treatment and post-treatment processes of the tumor growth, with the piecewise derivative, and to consider these processes as a whole thanks to this new concept. This concept leads us to analyze and predict the process from the beginning to the end of the tumor, as it offers the possibility to observe many behaviors from crossover to stochastic processes. Moreover, the piecewise differential operators, which can be constructed with operators such as classical, Caputo, Caputo-Fabrizio, Atangana-Baleanu and stochastic derivative, have opened new doors to readers in different disciplines and enable them to capture different behaviors in different time intervals. Thus, researchers can achieve successful results in capturing reality by applying these operators to real-world problems.
  • [ X ]
    Öğe
    Delay differential equations with fractional differential operators: Existence, uniqueness and applications to chaos
    (Amer Inst Mathematical Sciences-Aims, 2024) Arik, Irem Akbulut; Araz, Sedaigret
    In this study, we consider a chaotic model in which fractional differential operators and the delay term are added. Using the Carathe ' odory existence-uniqueness theorem for this chaotic model modified with the Caputo fractional derivative, we show that the solution of the associated system exists and is unique. We consider the chaotic model with a delay term with Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives and present a numerical algorithm for these models. We then present the numerical solution of chaotic models with delay terms by using piecewise differential operators, where fractional, classical and stochastic processes can be used. We present the numerical solution of chaotic models with delay terms, as modified by using piecewise differential operators. The graphical representations of these models are simulated for different values of the fractional order.
  • [ X ]
    Öğe
    Numerical simulation of Covid-19 model with integer and non-integer order: The effect of environment and social distancing
    (Elsevier, 2023) Arik, Irem Akbulut; Sari, Hatice Kuebra; Araz, Seda Igret
    We consider an epidemiological model that takes into account pathogens in the environment and social distancing. Such model with six classes has been updated with fractional differential operators and piecewise differential operators. Equilibrium points and reproductive number for the model have been obtained using next generation approach. Necessary optimality conditions for the model modified by addition of some control variables have been presented. For the numerical solution of the model, a numerical method based on Newton polynomial has been considered. The graphical representations for the model with fractional and piecewise derivatives have been presented to better understand the dynamic of model incorporating environment and social distancing.
  • [ X ]
    Öğe
    ON THE PERIODIC SOLUTIONS OF NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS VIA FIXED POINT METHOD
    (Univ Prishtines, 2022) Arik, Irem Akbulut; Tunc, Cemil
    In the present article, we study existence of periodic solutions (EPSs) of a nonlinear neutral integro- differential equation (NIDE) with multiple variable delays using Krasnoselskiis fixed point theorem. Transforming the considered NIDE to an equivalent integral equation, we prove the EPSs using a fixed point mapping, which is defined as a sum of a contraction and a compact map. The result of this paper has contributions to the topic of the EPSs of NIDEs.