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    Analysis and numerical computations of the fractional regularized long-wave equation with damping term
    (Wiley, 2021) Yavuz, Mehmet; Sulaiman, Tukur Abdulkadir; Usta, Fuat; Bulut, Hasan
    This study explores the fractional damped generalized regularized long-wave equation in the sense of Caputo, Atangana-Baleanu, and Caputo-Fabrizio fractional derivatives. With the aid of fixed-point theorem in the Atangana-Baleanu fractional derivative with Mittag-Leffler-type kernel, we show the existence and uniqueness of the solution to the damped generalized regularized long-wave equation. The modified Laplace decomposition method (MLDM) defined in the sense of Caputo, Atangana-Baleanu, and Caputo-Fabrizio (in the Riemann sense) operators is used in securing the approximate-analytical solutions of the nonlinear model. The numerical simulations of the obtained solutions are performed with different suitable values of rho, which is the order of fractional parameter. We have seen the effect of the various parameters and variables on the displacement in figures.
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    Importance of modelling and simulation in biophysical applications
    (Amer Inst Mathematical Sciences-Aims, 2023) Yavuz, Mehmet; Usta, Fuat
    Mathematical modelling and simulation in biophysics and its applications in terms of both theoretical and biological/physical/ecological point of view arise in a number of research problems ranging from physical and chemical processes to biomathematics and life science. As known, the modeling of a biophysical system requires the analysis of the different interactions occurring among the different components of the system. This editorial article deals with the topic of this special issue, which is devoted to the new developments in the modelling and simulation in biophysical applications with special attention to the interplay between different scholars.