Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method
In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the pro...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/21/6/597 |
| _version_ | 1811185309411442688 |
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| author | Hassan Khan Rasool Shah Poom Kumam Muhammad Arif |
| author_facet | Hassan Khan Rasool Shah Poom Kumam Muhammad Arif |
| author_sort | Hassan Khan |
| collection | DOAJ |
| description | In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to be one of the best analytical techniques, in order to solve fractional-order linear and nonlinear Partial deferential equations, particularly fractional-order heat and wave equation. |
| first_indexed | 2024-04-11T13:27:19Z |
| format | Article |
| id | doaj.art-ef1502fde3f94aa9a2d49346278d6c15 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:27:19Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ef1502fde3f94aa9a2d49346278d6c152022-12-22T04:22:01ZengMDPI AGEntropy1099-43002019-06-0121659710.3390/e21060597e21060597Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition MethodHassan Khan0Rasool Shah1Poom Kumam2Muhammad Arif3Department of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanCenter of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanIn the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to be one of the best analytical techniques, in order to solve fractional-order linear and nonlinear Partial deferential equations, particularly fractional-order heat and wave equation.https://www.mdpi.com/1099-4300/21/6/597natural transform decomposition methodfractional-order heat and wave equationsCaputo operator |
| spellingShingle | Hassan Khan Rasool Shah Poom Kumam Muhammad Arif Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method Entropy natural transform decomposition method fractional-order heat and wave equations Caputo operator |
| title | Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method |
| title_full | Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method |
| title_fullStr | Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method |
| title_full_unstemmed | Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method |
| title_short | Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method |
| title_sort | analytical solutions of fractional order heat and wave equations by the natural transform decomposition method |
| topic | natural transform decomposition method fractional-order heat and wave equations Caputo operator |
| url | https://www.mdpi.com/1099-4300/21/6/597 |
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