Theoretical and numerical aspects of the Malaria transmission model with piecewise technique
In this paper, we apply piecewise derivatives with both singular and non-singular kernels to investigate a malaria model. The singular kernel is the Caputo derivative, while the non-singular kernel is the Atangana-Baleanu operator in Caputo's sense (ABC). The existence, uniqueness, and numerica...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-10-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231451?viewType=HTML |
| _version_ | 1797635348030816256 |
|---|---|
| author | Shakeel Muhammad Obaid J. Algahtani Sayed Saifullah Amir Ali |
| author_facet | Shakeel Muhammad Obaid J. Algahtani Sayed Saifullah Amir Ali |
| author_sort | Shakeel Muhammad |
| collection | DOAJ |
| description | In this paper, we apply piecewise derivatives with both singular and non-singular kernels to investigate a malaria model. The singular kernel is the Caputo derivative, while the non-singular kernel is the Atangana-Baleanu operator in Caputo's sense (ABC). The existence, uniqueness, and numerical algorithm of the proposed model are presented using piecewise derivatives with both kernels. The stability is also presented for the proposed model using Ulam-Hyers stability. The numerical simulations are performed considering different fractional orders and compared the results with the real data to evaluate the efficiency of the proposed approach. |
| first_indexed | 2024-03-11T12:20:54Z |
| format | Article |
| id | doaj.art-888c636c831b4d61b6028d8bf9ad7fe3 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T12:20:54Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-888c636c831b4d61b6028d8bf9ad7fe32023-11-07T01:13:20ZengAIMS PressAIMS Mathematics2473-69882023-10-01812283532837510.3934/math.20231451Theoretical and numerical aspects of the Malaria transmission model with piecewise techniqueShakeel Muhammad0Obaid J. Algahtani 1Sayed Saifullah2Amir Ali31. Department of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhwa, Pakistan2. Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia1. Department of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhwa, Pakistan1. Department of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhwa, PakistanIn this paper, we apply piecewise derivatives with both singular and non-singular kernels to investigate a malaria model. The singular kernel is the Caputo derivative, while the non-singular kernel is the Atangana-Baleanu operator in Caputo's sense (ABC). The existence, uniqueness, and numerical algorithm of the proposed model are presented using piecewise derivatives with both kernels. The stability is also presented for the proposed model using Ulam-Hyers stability. The numerical simulations are performed considering different fractional orders and compared the results with the real data to evaluate the efficiency of the proposed approach.https://www.aimspress.com/article/doi/10.3934/math.20231451?viewType=HTMLpiecewise operatorcaputo and atangana-baleanu operatorsmalaria mathematical model |
| spellingShingle | Shakeel Muhammad Obaid J. Algahtani Sayed Saifullah Amir Ali Theoretical and numerical aspects of the Malaria transmission model with piecewise technique AIMS Mathematics piecewise operator caputo and atangana-baleanu operators malaria mathematical model |
| title | Theoretical and numerical aspects of the Malaria transmission model with piecewise technique |
| title_full | Theoretical and numerical aspects of the Malaria transmission model with piecewise technique |
| title_fullStr | Theoretical and numerical aspects of the Malaria transmission model with piecewise technique |
| title_full_unstemmed | Theoretical and numerical aspects of the Malaria transmission model with piecewise technique |
| title_short | Theoretical and numerical aspects of the Malaria transmission model with piecewise technique |
| title_sort | theoretical and numerical aspects of the malaria transmission model with piecewise technique |
| topic | piecewise operator caputo and atangana-baleanu operators malaria mathematical model |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231451?viewType=HTML |
| work_keys_str_mv | AT shakeelmuhammad theoreticalandnumericalaspectsofthemalariatransmissionmodelwithpiecewisetechnique AT obaidjalgahtani theoreticalandnumericalaspectsofthemalariatransmissionmodelwithpiecewisetechnique AT sayedsaifullah theoreticalandnumericalaspectsofthemalariatransmissionmodelwithpiecewisetechnique AT amirali theoreticalandnumericalaspectsofthemalariatransmissionmodelwithpiecewisetechnique |