A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability
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 con...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4369 |
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| author | Sina Etemad Albert Shikongo Kolade M. Owolabi Brahim Tellab İbrahim Avcı Shahram Rezapour Ravi P. Agarwal |
| author_facet | Sina Etemad Albert Shikongo Kolade M. Owolabi Brahim Tellab İbrahim Avcı Shahram Rezapour Ravi P. Agarwal |
| author_sort | Sina Etemad |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T18:10:30Z |
| format | Article |
| id | doaj.art-0b25894cc676419585778617a0b84924 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:10:30Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0b25894cc676419585778617a0b849242023-11-24T09:10:30ZengMDPI AGMathematics2227-73902022-11-011022436910.3390/math10224369A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical StabilitySina Etemad0Albert Shikongo1Kolade M. Owolabi2Brahim Tellab3İbrahim Avcı4Shahram Rezapour5Ravi P. Agarwal6Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, IranEngineering Mathematics, School of Engineering, University of Namibia, Windhoek 13301, NamibiaDepartment of Mathematical Sciences, Federal University of Technology, Akure PMB 704, NigeriaLaboratory of Applied Mathematics, Kasdi Merbah University, Ouargla 30000, AlgeriaDepartment of Computer Engineering, Faculty of Engineering, Final International University, via Mersin 10, Kyrenia 99300, Northern Cyprus, TurkeyDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, IranDepartment of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USAIn 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.https://www.mdpi.com/2227-7390/10/22/4369hybrid fractal-fractional derivativesmoking modelapproximate solutionstabilitysensitivity analysisLagrangian piece-wise interpolation |
| spellingShingle | Sina Etemad Albert Shikongo Kolade M. Owolabi Brahim Tellab İbrahim Avcı Shahram Rezapour Ravi P. Agarwal A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability Mathematics hybrid fractal-fractional derivative smoking model approximate solution stability sensitivity analysis Lagrangian piece-wise interpolation |
| title | A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability |
| title_full | A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability |
| title_fullStr | A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability |
| title_full_unstemmed | A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability |
| title_short | A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability |
| title_sort | new fractal fractional version of giving up smoking model application of lagrangian piece wise interpolation along with asymptotical stability |
| topic | hybrid fractal-fractional derivative smoking model approximate solution stability sensitivity analysis Lagrangian piece-wise interpolation |
| url | https://www.mdpi.com/2227-7390/10/22/4369 |
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