A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations
Usually, to find the analytical and numerical solution of the boundary value problems of fractional partial differential equations is not an easy task; however, the researchers devoted their sincere attempt to find the solutions of various equations by using either analytical or numerical procedures...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-08-01
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| Series: | Open Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/phys-2022-0072 |
| _version_ | 1797998614445817856 |
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| author | Khan Hassan Hajira Khan Qasim Kumam Poom Tchier Fairouz Singh Gurpreet Sitthithakerngkiet Kanokwan Tawfiq Ferdous Mohammed |
| author_facet | Khan Hassan Hajira Khan Qasim Kumam Poom Tchier Fairouz Singh Gurpreet Sitthithakerngkiet Kanokwan Tawfiq Ferdous Mohammed |
| author_sort | Khan Hassan |
| collection | DOAJ |
| description | Usually, to find the analytical and numerical solution of the boundary value problems of fractional partial differential equations is not an easy task; however, the researchers devoted their sincere attempt to find the solutions of various equations by using either analytical or numerical procedures. In this article, a very accurate and prominent method is developed to find the analytical solution of hyperbolic-telegraph equations with initial and boundary conditions within the Caputo operator, which has very simple calculations. This method is called a new technique of Adomian decomposition method. The obtained results are described by plots to confirm the accuracy of the suggested technique. Plots are drawn for both fractional and integer order solutions to confirm the accuracy and validity of the proposed method. Solutions are obtained at different fractional orders to discuss the useful dynamics of the targeted problems. Moreover, the suggested technique has provided the highest accuracy with a small number of calculations. The suggested technique gives results in the form of a series of solutions with easily computable and convergent components. The method is simple and straightforward and therefore preferred for the solutions of other problems with both initial and boundary conditions. |
| first_indexed | 2024-04-11T10:51:30Z |
| format | Article |
| id | doaj.art-cf2e06bdad1a4de2a3141e8b5eebbbc6 |
| institution | Directory Open Access Journal |
| issn | 2391-5471 |
| language | English |
| last_indexed | 2024-04-11T10:51:30Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj.art-cf2e06bdad1a4de2a3141e8b5eebbbc62022-12-22T04:28:54ZengDe GruyterOpen Physics2391-54712022-08-0120176477710.1515/phys-2022-0072A new modified technique to study the dynamics of fractional hyperbolic-telegraph equationsKhan Hassan0Hajira1Khan Qasim2Kumam Poom3Tchier Fairouz4Singh Gurpreet5Sitthithakerngkiet Kanokwan6Tawfiq Ferdous Mohammed7Department of Mathematics, Abdul Wali khan University Mardan, Mardan, PakistanDepartment of Mathematics, Abdul Wali khan University Mardan, Mardan, PakistanDepartment of Mathematics, Abdul Wali khan University Mardan, Mardan, PakistanCenter of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang ModThung Khru, Bangkok 10140, ThailandDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaSchool of Mathematical Sciences, Dublin City University, Dublin, IrelandDepartment of Mathematics, Intelligent and Nonlinear Dynamic Innovations Research Center, Faculty of Applied Science, King Mongkut’s University of Technology, North Bangkok (KMUTNB), 1518, Wongsawang, Bangsue, Bangkok 10800, ThailandDepartment of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi ArabiaUsually, to find the analytical and numerical solution of the boundary value problems of fractional partial differential equations is not an easy task; however, the researchers devoted their sincere attempt to find the solutions of various equations by using either analytical or numerical procedures. In this article, a very accurate and prominent method is developed to find the analytical solution of hyperbolic-telegraph equations with initial and boundary conditions within the Caputo operator, which has very simple calculations. This method is called a new technique of Adomian decomposition method. The obtained results are described by plots to confirm the accuracy of the suggested technique. Plots are drawn for both fractional and integer order solutions to confirm the accuracy and validity of the proposed method. Solutions are obtained at different fractional orders to discuss the useful dynamics of the targeted problems. Moreover, the suggested technique has provided the highest accuracy with a small number of calculations. The suggested technique gives results in the form of a series of solutions with easily computable and convergent components. The method is simple and straightforward and therefore preferred for the solutions of other problems with both initial and boundary conditions.https://doi.org/10.1515/phys-2022-0072adomian decomposition methodinitial-boundary value problemsfractional hyperbolic-telegraph equations |
| spellingShingle | Khan Hassan Hajira Khan Qasim Kumam Poom Tchier Fairouz Singh Gurpreet Sitthithakerngkiet Kanokwan Tawfiq Ferdous Mohammed A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations Open Physics adomian decomposition method initial-boundary value problems fractional hyperbolic-telegraph equations |
| title | A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations |
| title_full | A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations |
| title_fullStr | A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations |
| title_full_unstemmed | A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations |
| title_short | A new modified technique to study the dynamics of fractional hyperbolic-telegraph equations |
| title_sort | new modified technique to study the dynamics of fractional hyperbolic telegraph equations |
| topic | adomian decomposition method initial-boundary value problems fractional hyperbolic-telegraph equations |
| url | https://doi.org/10.1515/phys-2022-0072 |
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