A numerical study of dengue internal transmission model with fractional piecewise derivative
The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Ba...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-08-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722004570 |
| _version_ | 1818473947822292992 |
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| author | Shabir Ahmad Mansour F. Yassen Mohammad Mahtab Alam Soliman Alkhati Fahd Jarad Muhammad Bilal Riaz |
| author_facet | Shabir Ahmad Mansour F. Yassen Mohammad Mahtab Alam Soliman Alkhati Fahd Jarad Muhammad Bilal Riaz |
| author_sort | Shabir Ahmad |
| collection | DOAJ |
| description | The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem’s approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer. |
| first_indexed | 2024-04-14T04:29:46Z |
| format | Article |
| id | doaj.art-97dc338f039243c9b1e626f84ca4ed2a |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-14T04:29:46Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-97dc338f039243c9b1e626f84ca4ed2a2022-12-22T02:12:07ZengElsevierResults in Physics2211-37972022-08-0139105798A numerical study of dengue internal transmission model with fractional piecewise derivativeShabir Ahmad0Mansour F. Yassen1Mohammad Mahtab Alam2Soliman Alkhati3Fahd Jarad4Muhammad Bilal Riaz5Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia; Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517 Damietta, EgyptDepartment of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, Abha 61421, Saudi ArabiaEngineering Math and Physics Department, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, EgyptDepartment of Mathematics, Cankaya University, Etimesgut 06790, Ankara, Turkey; Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Research, China Medical University, Taichung 40402, Taiwan; Corresponding author at: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924, Lodz, Poland.Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan; Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924, Lodz, Poland; Institute for Groundwater Studies, University of the Free State, Bloemfontein 9301, South Africa; Corresponding author at: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924, Lodz, Poland.The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem’s approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer.http://www.sciencedirect.com/science/article/pii/S2211379722004570Dengue modelPiecewise derivativeCaputo operatorAtangana–Baleanu operator |
| spellingShingle | Shabir Ahmad Mansour F. Yassen Mohammad Mahtab Alam Soliman Alkhati Fahd Jarad Muhammad Bilal Riaz A numerical study of dengue internal transmission model with fractional piecewise derivative Results in Physics Dengue model Piecewise derivative Caputo operator Atangana–Baleanu operator |
| title | A numerical study of dengue internal transmission model with fractional piecewise derivative |
| title_full | A numerical study of dengue internal transmission model with fractional piecewise derivative |
| title_fullStr | A numerical study of dengue internal transmission model with fractional piecewise derivative |
| title_full_unstemmed | A numerical study of dengue internal transmission model with fractional piecewise derivative |
| title_short | A numerical study of dengue internal transmission model with fractional piecewise derivative |
| title_sort | numerical study of dengue internal transmission model with fractional piecewise derivative |
| topic | Dengue model Piecewise derivative Caputo operator Atangana–Baleanu operator |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722004570 |
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