Numerical solution of two-dimensional fractional order Volterra integro-differential equations
The present paper is concerned with the implementation of the optimal homotopy asymptotic method to find the approximate solutions of two-dimensional fractional order Volterra integro-differential equations. The technique’s applicability and validity are tested through some numerical examples. The f...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2021-03-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0032636 |
| _version_ | 1818333063010058240 |
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| author | Sumbal Ahsan Rashid Nawaz Muhammad Akbar Kottakkaran Sooppy Nisar Kholod M. Abualnaja Emad E. Mahmoud Abdel-Haleem Abdel-Aty |
| author_facet | Sumbal Ahsan Rashid Nawaz Muhammad Akbar Kottakkaran Sooppy Nisar Kholod M. Abualnaja Emad E. Mahmoud Abdel-Haleem Abdel-Aty |
| author_sort | Sumbal Ahsan |
| collection | DOAJ |
| description | The present paper is concerned with the implementation of the optimal homotopy asymptotic method to find the approximate solutions of two-dimensional fractional order Volterra integro-differential equations. The technique’s applicability and validity are tested through some numerical examples. The fractional order derivatives are calculated using Caputo’s sense. Results obtained by the proposed technique are compared with the Legendre wavelet method. The proposed method provides us with efficient and more accurate solutions than the other existing methods in the literature. Error analysis and convergence of the proposed method are also provided in the paper. |
| first_indexed | 2024-12-13T13:45:40Z |
| format | Article |
| id | doaj.art-39f3a22db2934a8a98e69a3aad103355 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-13T13:45:40Z |
| publishDate | 2021-03-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-39f3a22db2934a8a98e69a3aad1033552022-12-21T23:43:25ZengAIP Publishing LLCAIP Advances2158-32262021-03-01113035232035232-1310.1063/5.0032636Numerical solution of two-dimensional fractional order Volterra integro-differential equationsSumbal Ahsan0Rashid Nawaz1Muhammad Akbar2Kottakkaran Sooppy Nisar3Kholod M. Abualnaja4Emad E. Mahmoud5Abdel-Haleem Abdel-Aty6Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa 23200, PakistanDepartment of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Mathematics, Faculty of Applied Science, Umm Al-Qura University, P.O. Box 14949, Makkah, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi ArabiaThe present paper is concerned with the implementation of the optimal homotopy asymptotic method to find the approximate solutions of two-dimensional fractional order Volterra integro-differential equations. The technique’s applicability and validity are tested through some numerical examples. The fractional order derivatives are calculated using Caputo’s sense. Results obtained by the proposed technique are compared with the Legendre wavelet method. The proposed method provides us with efficient and more accurate solutions than the other existing methods in the literature. Error analysis and convergence of the proposed method are also provided in the paper.http://dx.doi.org/10.1063/5.0032636 |
| spellingShingle | Sumbal Ahsan Rashid Nawaz Muhammad Akbar Kottakkaran Sooppy Nisar Kholod M. Abualnaja Emad E. Mahmoud Abdel-Haleem Abdel-Aty Numerical solution of two-dimensional fractional order Volterra integro-differential equations AIP Advances |
| title | Numerical solution of two-dimensional fractional order Volterra integro-differential equations |
| title_full | Numerical solution of two-dimensional fractional order Volterra integro-differential equations |
| title_fullStr | Numerical solution of two-dimensional fractional order Volterra integro-differential equations |
| title_full_unstemmed | Numerical solution of two-dimensional fractional order Volterra integro-differential equations |
| title_short | Numerical solution of two-dimensional fractional order Volterra integro-differential equations |
| title_sort | numerical solution of two dimensional fractional order volterra integro differential equations |
| url | http://dx.doi.org/10.1063/5.0032636 |
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