Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions
This research work addresses the numerical solutions of nonlinear fractional integro-differential equations with mixed boundary conditions, using Chebyshev wavelet method. The basic idea of this work started from the Caputo definition of fractional differential operator. The fractional derivatives a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2017-03-01
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| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1177/1687814017694802 |
| _version_ | 1818162854375718912 |
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| author | Syed Tauseef Mohyud-Din Hassan Khan Muhammad Arif Muhammad Rafiq |
| author_facet | Syed Tauseef Mohyud-Din Hassan Khan Muhammad Arif Muhammad Rafiq |
| author_sort | Syed Tauseef Mohyud-Din |
| collection | DOAJ |
| description | This research work addresses the numerical solutions of nonlinear fractional integro-differential equations with mixed boundary conditions, using Chebyshev wavelet method. The basic idea of this work started from the Caputo definition of fractional differential operator. The fractional derivatives are replaced by Caputo operator, and the solution is approximated by wavelet family of functions. The numerical scheme by Chebyshev wavelet method is constructed through a very simple and straightforward way. The numerical results of the current method are compared with the exact solutions of the problems, which show that the proposed method has a strong agreement with the exact solutions of the problems. The numerical solutions of the present method are also compared with steepest decent method and Adomian decomposition method. The comparison with other methods reveals that this method has the highest degree of accuracy than those methods. |
| first_indexed | 2024-12-11T16:40:17Z |
| format | Article |
| id | doaj.art-7c3d7be4d3f04a2589e72e9282b87eeb |
| institution | Directory Open Access Journal |
| issn | 1687-8140 |
| language | English |
| last_indexed | 2024-12-11T16:40:17Z |
| publishDate | 2017-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Advances in Mechanical Engineering |
| spelling | doaj.art-7c3d7be4d3f04a2589e72e9282b87eeb2022-12-22T00:58:21ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402017-03-01910.1177/1687814017694802Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditionsSyed Tauseef Mohyud-Din0Hassan Khan1Muhammad Arif2Muhammad Rafiq3Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, PakistanThis research work addresses the numerical solutions of nonlinear fractional integro-differential equations with mixed boundary conditions, using Chebyshev wavelet method. The basic idea of this work started from the Caputo definition of fractional differential operator. The fractional derivatives are replaced by Caputo operator, and the solution is approximated by wavelet family of functions. The numerical scheme by Chebyshev wavelet method is constructed through a very simple and straightforward way. The numerical results of the current method are compared with the exact solutions of the problems, which show that the proposed method has a strong agreement with the exact solutions of the problems. The numerical solutions of the present method are also compared with steepest decent method and Adomian decomposition method. The comparison with other methods reveals that this method has the highest degree of accuracy than those methods.https://doi.org/10.1177/1687814017694802 |
| spellingShingle | Syed Tauseef Mohyud-Din Hassan Khan Muhammad Arif Muhammad Rafiq Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions Advances in Mechanical Engineering |
| title | Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions |
| title_full | Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions |
| title_fullStr | Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions |
| title_full_unstemmed | Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions |
| title_short | Chebyshev wavelet method to nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions |
| title_sort | chebyshev wavelet method to nonlinear fractional volterra fredholm integro differential equations with mixed boundary conditions |
| url | https://doi.org/10.1177/1687814017694802 |
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