Yazar "Cetin, Mehmet Akif" seçeneğine göre listele

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    Öğe
    Existence, uniqueness and numerical solution of stochastic fractional differential equations with integer and non-integer orders
    (Amer Inst Mathematical Sciences-Aims, 2024) Araz, Seda I. G. R. E. T.; Cetin, Mehmet Akif; Atangana, Abdon
    The parametrized approach is extended in this study to find solutions to differential equations with fractal, fractional, fractal-fractional, and piecewise derivatives with the inclusion of a stochastic component. The existence and uniqueness of the solution to the stochastic Atangana-Baleanu fractional differential equation are established using Caratheodory's existence theorem. For the solution of differential equations using piecewise differential operators, which take into account combining deterministic and stochastic processes utilizing certain significant mathematical tools such as fractal and fractal-fractional derivatives, the applicability of the parametrized technique is being examined. We discuss the crossover behaviors of the model obtained by including these operators and we present some illustrative examples for some problems with piecewise differential operators.
  • [ X ]
    Öğe
    Prediction of COVID-19 spread with models in different patterns: A case study of Russia
    (De Gruyter Poland Sp Z O O, 2024) Cetin, Mehmet Akif; Araz, Seda Igret
    This study deals with a mathematical model that examines the spread of Coronavirus disease (COVID-19). This model has been handled with different processes such as deterministic, stochastic, and deterministic-stochastic. First of all, a detailed analysis is presented for the deterministic model, which includes the positivity of the solution, the basic reproduction number, the disease, and endemic equilibrium points. Then, for the stochastic model, we investigate under which conditions, the solution exists and is unique. Later, model is reconsidered with the help of the piecewise derivative, which can combine deterministic and stochastic processes. Numerical simulations are presented for all these processes. Finally, the model has been modified with the rate indicator function. The model presenting these four different situations is compared with the real data in Russia. According to the results obtained from these situations, the model that is obtained by adding the rate indicator function predicts the COVID-19 outbreak in Russia more accurately. Thus, it is concluded that the model with the rate indicator function presents more realistic approach than the previous ones.