A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient
The Ambartsumian delay differential equation with a variable coefficient is considered in this paper. An effective transformation is produced to convert the extended Ambartsumian equation to the pantograph model. Two kinds of analytical solutions are determined. The first solution is expressed as an...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241696 |
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| author | Rana M. S. Alyoubi Abdelhalim Ebaid Essam R. El-Zahar Mona D. Aljoufi |
| author_facet | Rana M. S. Alyoubi Abdelhalim Ebaid Essam R. El-Zahar Mona D. Aljoufi |
| author_sort | Rana M. S. Alyoubi |
| collection | DOAJ |
| description | The Ambartsumian delay differential equation with a variable coefficient is considered in this paper. An effective transformation is produced to convert the extended Ambartsumian equation to the pantograph model. Two kinds of analytical solutions are determined. The first solution is expressed as an exponential function multiplied by an infinite power series. The second solution is obtained as an infinite series in terms of exponential functions. Several exact solutions are established for different forms of the extended Ambartsumian equation under specific relations. In addition, the convergence analysis is addressed theoretically. Moreover, numeric calculations are conducted to estimate the accuracy. The results reveal that the present analysis is efficient and accurate and can be further applied to similar delay models in a straightforward manner. |
| format | Article |
| id | doaj-art-7801dbca74634cd5a9d49d523872b24a |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-7801dbca74634cd5a9d49d523872b24a2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912357433575810.3934/math.20241696A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficientRana M. S. Alyoubi0Abdelhalim Ebaid1Essam R. El-Zahar2Mona D. Aljoufi3Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaThe Ambartsumian delay differential equation with a variable coefficient is considered in this paper. An effective transformation is produced to convert the extended Ambartsumian equation to the pantograph model. Two kinds of analytical solutions are determined. The first solution is expressed as an exponential function multiplied by an infinite power series. The second solution is obtained as an infinite series in terms of exponential functions. Several exact solutions are established for different forms of the extended Ambartsumian equation under specific relations. In addition, the convergence analysis is addressed theoretically. Moreover, numeric calculations are conducted to estimate the accuracy. The results reveal that the present analysis is efficient and accurate and can be further applied to similar delay models in a straightforward manner.https://www.aimspress.com/article/doi/10.3934/math.20241696ambartsumian equationdelayexact solutionseries solution |
| spellingShingle | Rana M. S. Alyoubi Abdelhalim Ebaid Essam R. El-Zahar Mona D. Aljoufi A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient AIMS Mathematics ambartsumian equation delay exact solution series solution |
| title | A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient |
| title_full | A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient |
| title_fullStr | A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient |
| title_full_unstemmed | A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient |
| title_short | A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient |
| title_sort | novel analytical treatment for the ambartsumian delay differential equation with a variable coefficient |
| topic | ambartsumian equation delay exact solution series solution |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241696 |
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