A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets
In this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/3/2/30 |
| _version_ | 1818936362617798656 |
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| author | Dumitru Baleanu Hassan Kamil Jassim |
| author_facet | Dumitru Baleanu Hassan Kamil Jassim |
| author_sort | Dumitru Baleanu |
| collection | DOAJ |
| description | In this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is a combination of the local fractional Laplace transform (LFLT) and the homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique. |
| first_indexed | 2024-12-20T05:34:52Z |
| format | Article |
| id | doaj.art-a38408c2e7744882a3891cace83003e0 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-20T05:34:52Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-a38408c2e7744882a3891cace83003e02022-12-21T19:51:39ZengMDPI AGFractal and Fractional2504-31102019-06-01323010.3390/fractalfract3020030fractalfract3020030A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor SetsDumitru Baleanu0Hassan Kamil Jassim1Department of Mathematics, Faculty of Art and Sciences, Çankaya University, Ankara 06530, TurkeyDepartment of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah 64001, IraqIn this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is a combination of the local fractional Laplace transform (LFLT) and the homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.https://www.mdpi.com/2504-3110/3/2/30Helmholtz equationlocal fractional homotopy perturbation methodlocal fractional Laplace transformlocal fractional derivative operator |
| spellingShingle | Dumitru Baleanu Hassan Kamil Jassim A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets Fractal and Fractional Helmholtz equation local fractional homotopy perturbation method local fractional Laplace transform local fractional derivative operator |
| title | A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets |
| title_full | A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets |
| title_fullStr | A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets |
| title_full_unstemmed | A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets |
| title_short | A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets |
| title_sort | modification fractional homotopy perturbation method for solving helmholtz and coupled helmholtz equations on cantor sets |
| topic | Helmholtz equation local fractional homotopy perturbation method local fractional Laplace transform local fractional derivative operator |
| url | https://www.mdpi.com/2504-3110/3/2/30 |
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