Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations
In the current study, we solve two very important mathematical models, such as the time fractional-order space-fractional telegraph and diffusion-wave equations using a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and natural transfo...
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| 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/S2666818124003334 |
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| author | Nazek A. Obeidat Mahmoud S. Rawashdeh Malak Q. Al Erjani |
| author_facet | Nazek A. Obeidat Mahmoud S. Rawashdeh Malak Q. Al Erjani |
| author_sort | Nazek A. Obeidat |
| collection | DOAJ |
| description | In the current study, we solve two very important mathematical models, such as the time fractional-order space-fractional telegraph and diffusion-wave equations using a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and natural transform. The diffusion wave equation describes the flood wave propagation, which is used in solving overland and open channel flow problems. For this reason, it is critical to fully understand and effectively solve the diffusion wave equations. Because telegraph equations are crucial for modeling and developing voltage or frequency transmission, they are widely used in physics and engineering. Furthermore, the designing process is greatly impacted by the uncertainty in the system parameters. For nonlinear ordinary differential equations based on the theorem of Banach fixed point, we provide existence and uniqueness theorem proofs. The present approach has been successfully used to explore exact solutions for time fractional-order and space fractional-order applications. The results show how effective and valuable the ADNM. This paper presents a methodology that will be used in future work to address similar nonlinear problems related to fractional calculus. |
| format | Article |
| id | doaj-art-999be58368f54e4fa956e94d3ebd711d |
| 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-999be58368f54e4fa956e94d3ebd711d2025-08-20T02:50:13ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210094710.1016/j.padiff.2024.100947Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equationsNazek A. Obeidat0Mahmoud S. Rawashdeh1Malak Q. Al Erjani2Corresponding author.; Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, 22110, JordanDepartment of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, 22110, JordanDepartment of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, 22110, JordanIn the current study, we solve two very important mathematical models, such as the time fractional-order space-fractional telegraph and diffusion-wave equations using a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and natural transform. The diffusion wave equation describes the flood wave propagation, which is used in solving overland and open channel flow problems. For this reason, it is critical to fully understand and effectively solve the diffusion wave equations. Because telegraph equations are crucial for modeling and developing voltage or frequency transmission, they are widely used in physics and engineering. Furthermore, the designing process is greatly impacted by the uncertainty in the system parameters. For nonlinear ordinary differential equations based on the theorem of Banach fixed point, we provide existence and uniqueness theorem proofs. The present approach has been successfully used to explore exact solutions for time fractional-order and space fractional-order applications. The results show how effective and valuable the ADNM. This paper presents a methodology that will be used in future work to address similar nonlinear problems related to fractional calculus.http://www.sciencedirect.com/science/article/pii/S2666818124003334Liouville–Caputo fractional derivativeAdomian natural decomposition methodTelegraph equationDiffusion-wave equationBanach fixed point theorem |
| spellingShingle | Nazek A. Obeidat Mahmoud S. Rawashdeh Malak Q. Al Erjani Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations Partial Differential Equations in Applied Mathematics Liouville–Caputo fractional derivative Adomian natural decomposition method Telegraph equation Diffusion-wave equation Banach fixed point theorem |
| title | Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations |
| title_full | Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations |
| title_fullStr | Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations |
| title_full_unstemmed | Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations |
| title_short | Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations |
| title_sort | numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion wave equations |
| topic | Liouville–Caputo fractional derivative Adomian natural decomposition method Telegraph equation Diffusion-wave equation Banach fixed point theorem |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003334 |
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