Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations
This paper investigates fractional-order partial differential equations analytically by applying a modified technique called the Laplace residual power series method. The analytical solution was utilized to test the accuracy and precision of the proposed methodologies and shown by tables and graphs....
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023264?viewType=HTML |
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| author | M. Mossa Al-Sawalha Osama Y. Ababneh Rasool Shah Nehad Ali Shah Kamsing Nonlaopon |
| author_facet | M. Mossa Al-Sawalha Osama Y. Ababneh Rasool Shah Nehad Ali Shah Kamsing Nonlaopon |
| author_sort | M. Mossa Al-Sawalha |
| collection | DOAJ |
| description | This paper investigates fractional-order partial differential equations analytically by applying a modified technique called the Laplace residual power series method. The analytical solution was utilized to test the accuracy and precision of the proposed methodologies and shown by tables and graphs. The solution is a convergent series established on Taylor's new form. When determining the series coefficients like RPSM, the fractional derivatives must be calculated every time. We only need to perform a few computations to obtain the coefficients because LRPSM only requires the concept of an infinite limit. The advantage of this method is that it does not require Adomian polynomials or he's polynomials to solve nonlinear problems. As a result, the method's reduced computation size is a strength. The outcome we got supports the idea that the suggested method is the best one for handling any non-linear models that appear in technology and science. |
| first_indexed | 2024-04-10T19:52:56Z |
| format | Article |
| id | doaj.art-866c887c047440ceb2b3e2f0ad644f97 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T19:52:56Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-866c887c047440ceb2b3e2f0ad644f972023-01-28T01:20:28ZengAIMS PressAIMS Mathematics2473-69882023-01-01835266528010.3934/math.2023264Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equationsM. Mossa Al-Sawalha0Osama Y. Ababneh1Rasool Shah2Nehad Ali Shah 3Kamsing Nonlaopon 41. Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia2. Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan3. Department of Mathematics, Abdul Wali khan university Mardan, 23200, Pakistan4. Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea5. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandThis paper investigates fractional-order partial differential equations analytically by applying a modified technique called the Laplace residual power series method. The analytical solution was utilized to test the accuracy and precision of the proposed methodologies and shown by tables and graphs. The solution is a convergent series established on Taylor's new form. When determining the series coefficients like RPSM, the fractional derivatives must be calculated every time. We only need to perform a few computations to obtain the coefficients because LRPSM only requires the concept of an infinite limit. The advantage of this method is that it does not require Adomian polynomials or he's polynomials to solve nonlinear problems. As a result, the method's reduced computation size is a strength. The outcome we got supports the idea that the suggested method is the best one for handling any non-linear models that appear in technology and science.https://www.aimspress.com/article/doi/10.3934/math.2023264?viewType=HTMLresidual power seriesfractional-order partial differential equationslaplace transformcaputo operator |
| spellingShingle | M. Mossa Al-Sawalha Osama Y. Ababneh Rasool Shah Nehad Ali Shah Kamsing Nonlaopon Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations AIMS Mathematics residual power series fractional-order partial differential equations laplace transform caputo operator |
| title | Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations |
| title_full | Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations |
| title_fullStr | Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations |
| title_full_unstemmed | Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations |
| title_short | Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations |
| title_sort | combination of laplace transform and residual power series techniques of special fractional order non linear partial differential equations |
| topic | residual power series fractional-order partial differential equations laplace transform caputo operator |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023264?viewType=HTML |
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