On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method
In this paper, we discuss the existence and uniqueness of the solution of the second kind nonlinear Volterra-Fredholm integral equations (NV-FIEs) which appear in mathematical modeling of many phenomena, using Picard’s method. In addition, we use Banach fixed point theorem to show the solvability of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2022-07-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/2487 |
| _version_ | 1811265993472737280 |
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| author | A. S. Rahby M. A. Abdou G. A. Mosa |
| author_facet | A. S. Rahby M. A. Abdou G. A. Mosa |
| author_sort | A. S. Rahby |
| collection | DOAJ |
| description | In this paper, we discuss the existence and uniqueness of the solution of the second kind nonlinear Volterra-Fredholm integral equations (NV-FIEs) which appear in mathematical modeling of many phenomena, using Picard’s method. In addition, we use Banach fixed point theorem to show the solvability of the first kind NV-FIEs. Moreover, we utilize the homotopy analysis method (HAM) to approximate the solution and the convergence of the method is investigated. Finally, some examples are presented and the numerical results are discussed to show the validity of the theoretical results. |
| first_indexed | 2024-04-12T20:35:01Z |
| format | Article |
| id | doaj.art-8ca7078b946e47dea5261d6557d0182a |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-04-12T20:35:01Z |
| publishDate | 2022-07-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-8ca7078b946e47dea5261d6557d0182a2022-12-22T03:17:38ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392022-07-0120353510.28924/2291-8639-20-2022-351872On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis MethodA. S. RahbyM. A. AbdouG. A. MosaIn this paper, we discuss the existence and uniqueness of the solution of the second kind nonlinear Volterra-Fredholm integral equations (NV-FIEs) which appear in mathematical modeling of many phenomena, using Picard’s method. In addition, we use Banach fixed point theorem to show the solvability of the first kind NV-FIEs. Moreover, we utilize the homotopy analysis method (HAM) to approximate the solution and the convergence of the method is investigated. Finally, some examples are presented and the numerical results are discussed to show the validity of the theoretical results.http://etamaths.com/index.php/ijaa/article/view/2487 |
| spellingShingle | A. S. Rahby M. A. Abdou G. A. Mosa On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method International Journal of Analysis and Applications |
| title | On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method |
| title_full | On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method |
| title_fullStr | On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method |
| title_full_unstemmed | On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method |
| title_short | On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method |
| title_sort | on the solutions of the second kind nonlinear volterra fredholm integral equations via homotopy analysis method |
| url | http://etamaths.com/index.php/ijaa/article/view/2487 |
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