Alzaid, Sara S.; Chauhan, R. P.; Kumar, Sunil; Alkahtani, Badr Saad T. A high order numerical scheme for fractal-fractional laser system with chaos study. (English) Zbl 1504.34109 Fractals 30, No. 5, Article ID 2240183, 19 p. (2022). Summary: The primary goal of this research is to look into the dynamical behavior of a fractional and fractal-fractional (FF) order laser chaotic model. The model is first considered with Caputo’s fractional derivative. An iterative technique based on the Laplace transform and its inverse aspect is used to achieve a particular solution for the fractional model. The existence of a unique solution is examined for the fractional laser chaotic model. Next, the laser chaotic model is addressed with a FF approach in the Caputo sense. The approximate results are achieved for the proposed fractional and FF models by using the Atangana-Seda numerical methods. The dynamical structures are plotted at various values of fractional and FF parameters. MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 78A60 Lasers, masers, optical bistability, nonlinear optics 34C28 Complex behavior and chaotic systems of ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A08 Fractional ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations Keywords:laser chaotic system; Caputo derivative; fractal-fractional derivative; numerical simulation PDFBibTeX XMLCite \textit{S. S. Alzaid} et al., Fractals 30, No. 5, Article ID 2240183, 19 p. (2022; Zbl 1504.34109) Full Text: DOI References: [1] Singh, J., Kumar, D., Al Qurashi, M. and Baleanu, D., A new fractional model for giving up smoking dynamics, Adv. Differ. Equ.2017(1) (2017) 88. · Zbl 1422.34062 [2] Gómez-Aguilar, J. F., López-López, M. G., Alvarado-Martínez, V. 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