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    Exploring the Dynamics of Measles Infection: A Fractional Calculus Approach to Stochastic Modeling
    (Matematikçiler Derneği, 2025) Çetin, Mehmet Akif; Araz, Seda İğret
    This article develops and analyzes a measles infection model using fractional calculus and stochastic methods. The existence and uniqueness of solutions are proven by verifying linear growth and Lipschitz conditions. The model, formulated with the Caputo fractional derivative, is numerically solved via the Newton polynomial method. Simulations illustrate the dynamics of measles infections, offering valuable theoretical and numerical insights that enhance understanding of infectious disease modeling.
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    Fractal-Fractional Modeling of the Covid-19 Spread with Deterministic and Stochastic Approaches
    (Springer, 2025) Igret Araz, Seda; Çetin, Mehmet Akif
    It is important to note that the process related to Covid-19 may exhibit random behavior due to environmental noise, and this factor should be taken into account. As a result, the modified Covid-19 model is evaluated using fractal-fractional derivatives in the sense of Caputo–Fabrizio, Caputo, and Atangana–Baleanu within a stochastic framework, aiming to create a more accurate representation of the Covid-19 outbreak. Mathematical analysis, including equilibrium points, the positivity of solutions, and the basic reproduction number for the deterministic model, is included in the study. The existence and uniqueness of solutions for the stochastic model are investigated under certain conditions. Additionally, the conditions for the existence of a global solution of the stochastic model are deduced, and the extinction of the infection within the model is studied. The outcomes of this model, incorporating memory effects, stochastic processes, and fractal properties, are supported by numerical simulations. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.
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    Numerical solution of a multi-wing chaotic system with piecewise differential operators
    (Abdus Salam School of mathematical Sciences, 2024) Çetin, Mehmet Akif; Genc, Selahattin; Araz, Metin
    In this study, a multi-wing chaotic system with classical derivative has been studied. The conditions under which the existence and uniqueness of the solution of this chaotic system exist are examined. Afterwards, this chaotic system has been modified using fractional differential operators, and in this case the behavior of the multi-wing chaotic system has been investigated. Moreover, the newly introduced piecewise differential operators is included in such a chaotic system and the piecewise chaotic system is solved by using Newton polynomial approach. The numerical simulations of piecewise chaotic system are performed for fractional order. © (2023), (Abdus Salam School of mathematical Sciences). All Rights Reserved.