Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves
An approximative procedure named asymptotic homotopy perturbation method (AHPM) is introduced to obtain solutions of the non-linear fractional order models. The two special cases, FZK(3; 3; 3) and FZK(2; 2; 2) of fractional Zakharov-Kuznetsov equations are chosen for the illustrative purpose of our...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2019.3.721/fulltext.html |
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| author | Samia Bushnaq Sajjad Ali Kamal Shah Muhammad Arif |
| author_facet | Samia Bushnaq Sajjad Ali Kamal Shah Muhammad Arif |
| author_sort | Samia Bushnaq |
| collection | DOAJ |
| description | An approximative procedure named asymptotic homotopy perturbation method (AHPM) is introduced to obtain solutions of the non-linear fractional order models. The two special cases, FZK(3; 3; 3) and FZK(2; 2; 2) of fractional Zakharov-Kuznetsov equations are chosen for the illustrative purpose of our method. AHPM is a very recent new procedure as compare with other existing homotopy perturbation procedures. A new auxiliary function has been introduced in AHPM. The AHPM solutions are compared with solutions of fractional complex transform FCT using variational iteration method VIM and exact solutions. Further, the surface graph of AHPM solutions are compared with surface graph of solutions of homotopy perturbation transform method (HPTM) solutions. In comparison, the solutions computed by AHPM are in agreement with exact solutions of the problems. The simulation section reveals that our new developed procedure is effective and explicit. |
| first_indexed | 2024-12-11T10:07:29Z |
| format | Article |
| id | doaj.art-3b2ab0fc16f448979ee3745b5359ebdc |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T10:07:29Z |
| publishDate | 2019-06-01 |
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| series | AIMS Mathematics |
| spelling | doaj.art-3b2ab0fc16f448979ee3745b5359ebdc2022-12-22T01:11:52ZengAIMS PressAIMS Mathematics2473-69882019-06-014372173910.3934/math.2019.3.721Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic wavesSamia Bushnaq0Sajjad Ali1Kamal Shah2Muhammad Arif31 Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, Jordan2 Department of Mathematics, Shaheed Benazir Bhutto University Sheringal Dir(U), Khyber Pakhtunkhwa, Pakistan 4 Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan3 Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan4 Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, PakistanAn approximative procedure named asymptotic homotopy perturbation method (AHPM) is introduced to obtain solutions of the non-linear fractional order models. The two special cases, FZK(3; 3; 3) and FZK(2; 2; 2) of fractional Zakharov-Kuznetsov equations are chosen for the illustrative purpose of our method. AHPM is a very recent new procedure as compare with other existing homotopy perturbation procedures. A new auxiliary function has been introduced in AHPM. The AHPM solutions are compared with solutions of fractional complex transform FCT using variational iteration method VIM and exact solutions. Further, the surface graph of AHPM solutions are compared with surface graph of solutions of homotopy perturbation transform method (HPTM) solutions. In comparison, the solutions computed by AHPM are in agreement with exact solutions of the problems. The simulation section reveals that our new developed procedure is effective and explicit.https://www.aimspress.com/article/10.3934/math.2019.3.721/fulltext.htmlasymptotic homotopy perturbation methodfractional Zakharov-Kuznetsov equations |
| spellingShingle | Samia Bushnaq Sajjad Ali Kamal Shah Muhammad Arif Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves AIMS Mathematics asymptotic homotopy perturbation method fractional Zakharov-Kuznetsov equations |
| title | Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves |
| title_full | Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves |
| title_fullStr | Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves |
| title_full_unstemmed | Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves |
| title_short | Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves |
| title_sort | approximate solutions to nonlinear fractional order partial differential equations arising in ion acoustic waves |
| topic | asymptotic homotopy perturbation method fractional Zakharov-Kuznetsov equations |
| url | https://www.aimspress.com/article/10.3934/math.2019.3.721/fulltext.html |
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