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    Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe
    (Springer, 2021) Atangana, Abdon; Igret Araz, Seda
    Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in the worse scenario and an exponential growth in the number of infections in Africa. The projection of statistical analysis leads us to introducing an extended version of the well-blancmange function to further capture the spread with fractal properties. A mathematical model depicting the spread with nine sub-classes is considered, first converted to a stochastic system, where the existence and uniqueness are presented. Then the model is extended to the concept of nonlocal operators; due to nonlinearity, a modified numerical scheme is suggested and used to present numerical simulations. The suggested mathematical model is able to predict two to three waves of the spread in the near future.
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    Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators
    (Pergamon-Elsevier Science Ltd, 2020) Igret Araz, Seda
    In this paper, we suggest a new integro-differential equation by utilizing from the concept of fractal-fractional derivative and integral newly introduced by Atangana. We offer that under which conditions the solution of the suggested equation is exist and unique benefitting from Banach fixed-point theorem. Also, we construct a new numerical scheme for the numerical solution of our problem and we give numerical simulation and illustrations for different values of fractional order alpha and fractal order beta. That's why, this study will guide for researchers significantly in theory and applications. (C) 2019 Elsevier Ltd. All rights reserved.
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    Rhythmic behaviors of the human heart with piecewise derivative
    (Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Igret Araz, Seda
    It has been noticed that heartbeats can display different patterns according to situations faced by a human. It has been indicated that, those passages from one pattern to another cannot be modelled using a single differential operator, either classical, fractional, or stochastic. In 2021, alternative concepts were introduced and called piecewise differentiation and integration, these concepts were applied in several complex problems with great insight. It is strongly believed that such will be leading concepts to modelling real-world problems with crossover behaviors. Crossover behaviors have been observed in heart rhythm, therefore, in this paper, the well-known van Der Pol equation will be subjected to piecewise analysis. Several simulations will be obtained using a numerical scheme based on Newton polynomial interpolation. Obtained figures show real world behaviors of heart rhythm with piecewise patterns.