Presentation of the efficient scheme for solving fractional order telegraph problems
The Asymptotic Homotopy Perturbation Transform Method AHPTM is presented in this work. It is combined version of the Asymptotic Homotopy Perturbation Method AHPM and Laplace transformation. The focus of the work is the introduction of a new fast convergent scheme to obtain the solution of the fracti...
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| Format: | Article |
| 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/S2666818124003620 |
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| author | Wasim Sajjad Hussain Sajjad Ali Nahid Fatima Kamal Shah Thabet Abdeljawad |
| author_facet | Wasim Sajjad Hussain Sajjad Ali Nahid Fatima Kamal Shah Thabet Abdeljawad |
| author_sort | Wasim Sajjad Hussain |
| collection | DOAJ |
| description | The Asymptotic Homotopy Perturbation Transform Method AHPTM is presented in this work. It is combined version of the Asymptotic Homotopy Perturbation Method AHPM and Laplace transformation. The focus of the work is the introduction of a new fast convergent scheme to obtain the solution of the fractional partial differential equations. Therefore, the first demonstration of the AHPTM is present for the solution of space-fractional telegraph equation (SFTE) in this work. The Caputo version of fractional derivatives has been utilized. Three test problems of the important fractional telegraph model were solved by this proposed scheme. The scheme of AHPTM worked without exploiting Ji. Huan He polynomials or Adomian polynomials. This application was elaborated by providing error estimates, a graphical presentation and tabulation of the results obtained by AHPTM. The comparison of results obtained by AHPTM with exact results is provided which indicated the accuracy of the scheme. |
| format | Article |
| id | doaj-art-f9e26e33e3e34c64a636bf655b4588d8 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-f9e26e33e3e34c64a636bf655b4588d82024-12-13T11:05:48ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100976Presentation of the efficient scheme for solving fractional order telegraph problemsWasim Sajjad Hussain0Sajjad Ali1Nahid Fatima2Kamal Shah3Thabet Abdeljawad4Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, KPK, PakistanDepartment of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, KPK, Pakistan; Corresponding author.Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa; Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally, 32093, KuwaitThe Asymptotic Homotopy Perturbation Transform Method AHPTM is presented in this work. It is combined version of the Asymptotic Homotopy Perturbation Method AHPM and Laplace transformation. The focus of the work is the introduction of a new fast convergent scheme to obtain the solution of the fractional partial differential equations. Therefore, the first demonstration of the AHPTM is present for the solution of space-fractional telegraph equation (SFTE) in this work. The Caputo version of fractional derivatives has been utilized. Three test problems of the important fractional telegraph model were solved by this proposed scheme. The scheme of AHPTM worked without exploiting Ji. Huan He polynomials or Adomian polynomials. This application was elaborated by providing error estimates, a graphical presentation and tabulation of the results obtained by AHPTM. The comparison of results obtained by AHPTM with exact results is provided which indicated the accuracy of the scheme.http://www.sciencedirect.com/science/article/pii/S2666818124003620Asymptotic homotopy methodNumerical analysisCaputo derivativeFractional telegraph equation |
| spellingShingle | Wasim Sajjad Hussain Sajjad Ali Nahid Fatima Kamal Shah Thabet Abdeljawad Presentation of the efficient scheme for solving fractional order telegraph problems Partial Differential Equations in Applied Mathematics Asymptotic homotopy method Numerical analysis Caputo derivative Fractional telegraph equation |
| title | Presentation of the efficient scheme for solving fractional order telegraph problems |
| title_full | Presentation of the efficient scheme for solving fractional order telegraph problems |
| title_fullStr | Presentation of the efficient scheme for solving fractional order telegraph problems |
| title_full_unstemmed | Presentation of the efficient scheme for solving fractional order telegraph problems |
| title_short | Presentation of the efficient scheme for solving fractional order telegraph problems |
| title_sort | presentation of the efficient scheme for solving fractional order telegraph problems |
| topic | Asymptotic homotopy method Numerical analysis Caputo derivative Fractional telegraph equation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003620 |
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