Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate
This manuscript investigates fractal-fractional order smoking models with relapse and harmonic mean type incidence rate under the Caputo derivative. We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered syst...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6344079 |
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| _version_ | 1832561376993738752 |
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| author | Zareen A. Khan Mati ur Rahman Kamal Shah |
| author_facet | Zareen A. Khan Mati ur Rahman Kamal Shah |
| author_sort | Zareen A. Khan |
| collection | DOAJ |
| description | This manuscript investigates fractal-fractional order smoking models with relapse and harmonic mean type incidence rate under the Caputo derivative. We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered system, Ulam-Hyers (UH) approach is used. We compute the numerical solution by using fractional Adams-Bashforth method. For the simulation of the model, we consider different values of fractional order δ and fractal dimension θ by using some real values of the parameters. The proposed scheme is used to simulate the available data for some smoking community including potential, light, and quit smokers. Various graphical presentations are given to understand the dynamics of the model at various fractional orders. |
| format | Article |
| id | doaj-art-a2f5a47bece146588c6264f564de2754 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a2f5a47bece146588c6264f564de27542025-02-03T01:25:08ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/63440796344079Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence RateZareen A. Khan0Mati ur Rahman1Kamal Shah2Department of Mathematics, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi ArabiaDepartment of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, ChinaDepartment of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, PakistanThis manuscript investigates fractal-fractional order smoking models with relapse and harmonic mean type incidence rate under the Caputo derivative. We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered system, Ulam-Hyers (UH) approach is used. We compute the numerical solution by using fractional Adams-Bashforth method. For the simulation of the model, we consider different values of fractional order δ and fractal dimension θ by using some real values of the parameters. The proposed scheme is used to simulate the available data for some smoking community including potential, light, and quit smokers. Various graphical presentations are given to understand the dynamics of the model at various fractional orders.http://dx.doi.org/10.1155/2021/6344079 |
| spellingShingle | Zareen A. Khan Mati ur Rahman Kamal Shah Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate Journal of Function Spaces |
| title | Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate |
| title_full | Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate |
| title_fullStr | Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate |
| title_full_unstemmed | Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate |
| title_short | Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate |
| title_sort | study of a fractal fractional smoking models with relapse and harmonic mean type incidence rate |
| url | http://dx.doi.org/10.1155/2021/6344079 |
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