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Abstract
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Drugs have always been one of the most important concerns of families and government
officials at all times, and they have caused irreparable damage to the health of young people. Given
the importance of this great challenge, this article discusses a non-symmetric fractal-fractional order
ice-smoking mathematical model for the existence results, numerical results, and stability analysis. For
the existence of the solution of the given ice-smoking model, successive iterative sequences are defined.
The uniqueness of the solution Hyers–Ulam (HU) stability is established with the help of the existing
definitions and theorems in functional analysis. By the utilization of two-step Lagrange polynomials,
we provide numerical solutions and provide a comparative numerical analysis for different values of
the fractional order and fractal order. The numerical simulations show the applicability of the scheme
and future prediction and the effects of fractal-fractional orders simultaneously.
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