Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem
This work explores a new abstract model using multi-term fractional differential operator and delay effect. The model is defined by the existence of a delay parameter and insertion of multi term fractional differential operators in the input function. For the solution of the newly formulated problem...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-05-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824002382 |
| _version_ | 1797203082584522752 |
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| author | Hui Li Ghaus ur Rahman Humaira Naz J.F. Gómez-Aguilar |
| author_facet | Hui Li Ghaus ur Rahman Humaira Naz J.F. Gómez-Aguilar |
| author_sort | Hui Li |
| collection | DOAJ |
| description | This work explores a new abstract model using multi-term fractional differential operator and delay effect. The model is defined by the existence of a delay parameter and insertion of multi term fractional differential operators in the input function. For the solution of the newly formulated problem, we utilized fixed-point theorems, which provide a powerful analytical tool for establishing the existence and uniqueness of solutions in functional spaces. Additionally, we investigate the stability properties of the implicit multi-term fractional delay differential equation (IMTFDDE) and employ the concept of Ulam-Hyers stability to assess their behaviour. The Ulam-Hyers stability framework is a contemporary approach that characterizes the sensitivity of solutions in functional spaces. Furthermore, we use an example to show how to apply our results. Lastly, for the real implementation of this research endeavour, we provided a real model devoted to modeling the dispersion of pollutants in a river while accounting for delayed effects and strip boundary circumstances. |
| first_indexed | 2024-04-24T08:13:41Z |
| format | Article |
| id | doaj.art-2e26c6c58df04466a36dcaf3acbea048 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-24T08:13:41Z |
| publishDate | 2024-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-2e26c6c58df04466a36dcaf3acbea0482024-04-17T04:48:37ZengElsevierAlexandria Engineering Journal1110-01682024-05-0194122Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problemHui Li0Ghaus ur Rahman1Humaira Naz2J.F. Gómez-Aguilar3School of Management Sciences and Engineering, Anhui University of Finance and Economics, Benghu, 233030, ChinaDepartment of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, PakistanCentro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001 Col. Chamilpa, C.P. 62209 Cuernavaca, Morelos, Mexico; Corresponding author.This work explores a new abstract model using multi-term fractional differential operator and delay effect. The model is defined by the existence of a delay parameter and insertion of multi term fractional differential operators in the input function. For the solution of the newly formulated problem, we utilized fixed-point theorems, which provide a powerful analytical tool for establishing the existence and uniqueness of solutions in functional spaces. Additionally, we investigate the stability properties of the implicit multi-term fractional delay differential equation (IMTFDDE) and employ the concept of Ulam-Hyers stability to assess their behaviour. The Ulam-Hyers stability framework is a contemporary approach that characterizes the sensitivity of solutions in functional spaces. Furthermore, we use an example to show how to apply our results. Lastly, for the real implementation of this research endeavour, we provided a real model devoted to modeling the dispersion of pollutants in a river while accounting for delayed effects and strip boundary circumstances.http://www.sciencedirect.com/science/article/pii/S1110016824002382Multi term fractional DEsExistence & uniqueness of solutionFunctional stabilityDispersion of pollutants |
| spellingShingle | Hui Li Ghaus ur Rahman Humaira Naz J.F. Gómez-Aguilar Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem Alexandria Engineering Journal Multi term fractional DEs Existence & uniqueness of solution Functional stability Dispersion of pollutants |
| title | Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem |
| title_full | Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem |
| title_fullStr | Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem |
| title_full_unstemmed | Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem |
| title_short | Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem |
| title_sort | modeling of implicit multi term fractional delay differential equation application in pollutant dispersion problem |
| topic | Multi term fractional DEs Existence & uniqueness of solution Functional stability Dispersion of pollutants |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824002382 |
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