Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions
This research utilizes the Yang Hussein Jassim method (YHJM) approach to investigate the precise solutions of the space–time telegraph equation analytically (ST-TE). The Yang Hussein Jassim method (YHJM) approach is an innovative and appealing hybrid transformation integration method, effectively co...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001093 |
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| author | Naser Rhaif Swain Hassan Kamil Jassim |
| author_facet | Naser Rhaif Swain Hassan Kamil Jassim |
| author_sort | Naser Rhaif Swain |
| collection | DOAJ |
| description | This research utilizes the Yang Hussein Jassim method (YHJM) approach to investigate the precise solutions of the space–time telegraph equation analytically (ST-TE). The Yang Hussein Jassim method (YHJM) approach is an innovative and appealing hybrid transformation integration method, effectively combining the Hussein Jassim (HJM) and Yang transform (Ya). Through a simplified iterative process with minimal computational requirements, this approach quickly provides convergent, sequential solutions. The reliability of the method is demonstrated by applying it to two case studies of the ST-TE within the framework of the Tania derivative, which includes the definition of non-singular kernel functions. The study also includes extensive comparisons between approximate, exact, and relevant literature-based solutions to assess the technique’s accuracy and effectiveness. Visual depictions demonstrate the influence of fractional temporal and spatial parameters on the behavior of solutions. The results indicate that this approach is straightforward to apply and effective for analyzing intricate physical models described by nonlinear partial differential equations with fractional time terms. |
| format | Article |
| id | doaj-art-7d2c4ea18eb7422db1cdfe1f35f6a5d4 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-7d2c4ea18eb7422db1cdfe1f35f6a5d42025-08-20T03:53:31ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410118210.1016/j.padiff.2025.101182Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensionsNaser Rhaif Swain0Hassan Kamil Jassim1Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq; College of Technical Engineering, National University of Science and Technology, Thi-Qar, IraqDepartment of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq; Corresponding author.This research utilizes the Yang Hussein Jassim method (YHJM) approach to investigate the precise solutions of the space–time telegraph equation analytically (ST-TE). The Yang Hussein Jassim method (YHJM) approach is an innovative and appealing hybrid transformation integration method, effectively combining the Hussein Jassim (HJM) and Yang transform (Ya). Through a simplified iterative process with minimal computational requirements, this approach quickly provides convergent, sequential solutions. The reliability of the method is demonstrated by applying it to two case studies of the ST-TE within the framework of the Tania derivative, which includes the definition of non-singular kernel functions. The study also includes extensive comparisons between approximate, exact, and relevant literature-based solutions to assess the technique’s accuracy and effectiveness. Visual depictions demonstrate the influence of fractional temporal and spatial parameters on the behavior of solutions. The results indicate that this approach is straightforward to apply and effective for analyzing intricate physical models described by nonlinear partial differential equations with fractional time terms.http://www.sciencedirect.com/science/article/pii/S2666818125001093Caputo fractional derivativeHussein Jassim methodMultidimensional fractional telegraph equationYang transform |
| spellingShingle | Naser Rhaif Swain Hassan Kamil Jassim Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions Partial Differential Equations in Applied Mathematics Caputo fractional derivative Hussein Jassim method Multidimensional fractional telegraph equation Yang transform |
| title | Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions |
| title_full | Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions |
| title_fullStr | Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions |
| title_full_unstemmed | Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions |
| title_short | Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions |
| title_sort | innovation of yang hussein jassim s method in solving nonlinear telegraph equations across multiple dimensions |
| topic | Caputo fractional derivative Hussein Jassim method Multidimensional fractional telegraph equation Yang transform |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001093 |
| work_keys_str_mv | AT naserrhaifswain innovationofyanghusseinjassimsmethodinsolvingnonlineartelegraphequationsacrossmultipledimensions AT hassankamiljassim innovationofyanghusseinjassimsmethodinsolvingnonlineartelegraphequationsacrossmultipledimensions |