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Abstract
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In this paper, a new kind of mathematical modeling is studied by providing a fivecompartmental
system of differential equations with respect to new hybrid generalized fractalfractional
derivatives. For the first time, we design a model of giving up smoking to analyze its
dynamical behaviors by considering two parameters of such generalized operators; i.e., fractal dimension
and fractional order. We apply a special sub-category of increasing functions to investigate the
existence of solutions. Uniqueness property is derived by a standard method based on the Lipschitz
rule. After proving stability property, the equilibrium points are obtained and asymptotically stable
solutions are studied. Finally, we illustrate all analytical results and findings via numerical algorithms
and graphs obtained by Lagrangian piece-wise interpolation, and discuss all behaviors of the relevant
solutions in the fractal-fractional system.
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