A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability

Sina Etemad (), Albert Shikongo, Kolade M. Owolabi, Brahim Tellab, İbrahim Avcı, Shahram Rezapour () and Ravi P. Agarwal ()
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Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Albert Shikongo: Engineering Mathematics, School of Engineering, University of Namibia, Windhoek 13301, Namibia
Kolade M. Owolabi: Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, Nigeria
Brahim Tellab: Laboratory of Applied Mathematics, Kasdi Merbah University, Ouargla 30000, Algeria
İbrahim Avcı: Department of Computer Engineering, Faculty of Engineering, Final International University, via Mersin 10, Kyrenia 99300, Northern Cyprus, Turkey
Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Ravi P. Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA

Mathematics, 2022, vol. 10, issue 22, 1-31

Abstract: In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional 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.

Keywords: hybrid fractal-fractional derivative; smoking model; approximate solution; stability; sensitivity analysis; Lagrangian piece-wise interpolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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