Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method
In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establ...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003255 |
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| author | S. Dhivya V. Govindan Choonkil Park Siriluk Donganont |
| author_facet | S. Dhivya V. Govindan Choonkil Park Siriluk Donganont |
| author_sort | S. Dhivya |
| collection | DOAJ |
| description | In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models. |
| format | Article |
| id | doaj-art-341d10ba73414fdf866fe0877a3df1db |
| institution | DOAJ |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-341d10ba73414fdf866fe0877a3df1db2025-08-20T02:50:13ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210093910.1016/j.padiff.2024.100939Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point methodS. Dhivya0V. Govindan1Choonkil Park2Siriluk Donganont3Department of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam 603103, Tamil Nadu, IndiaDepartment of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam 603103, Tamil Nadu, India; Corresponding author.Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of KoreaSchool of Science, University of Phayao, Phayao 56000, ThailandIn this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.http://www.sciencedirect.com/science/article/pii/S2666818124003255Nipah virusFractional modelABC fractional derivativeHyers–Ulam stabilityfixed point method |
| spellingShingle | S. Dhivya V. Govindan Choonkil Park Siriluk Donganont Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method Partial Differential Equations in Applied Mathematics Nipah virus Fractional model ABC fractional derivative Hyers–Ulam stability fixed point method |
| title | Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method |
| title_full | Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method |
| title_fullStr | Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method |
| title_full_unstemmed | Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method |
| title_short | Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method |
| title_sort | hyers ulam stability of nipah virus model using atangana baleanu caputo fractional derivative with fixed point method |
| topic | Nipah virus Fractional model ABC fractional derivative Hyers–Ulam stability fixed point method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003255 |
| work_keys_str_mv | AT sdhivya hyersulamstabilityofnipahvirusmodelusingatanganabaleanucaputofractionalderivativewithfixedpointmethod AT vgovindan hyersulamstabilityofnipahvirusmodelusingatanganabaleanucaputofractionalderivativewithfixedpointmethod AT choonkilpark hyersulamstabilityofnipahvirusmodelusingatanganabaleanucaputofractionalderivativewithfixedpointmethod AT sirilukdonganont hyersulamstabilityofnipahvirusmodelusingatanganabaleanucaputofractionalderivativewithfixedpointmethod |