Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators
The exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept, we used the decomposition method along with natur...
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| Format: | Article |
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MDPI AG
2023-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/233 |
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| author | Meshari Alesemi Jameelah S. Al Shahrani Naveed Iqbal Rasool Shah Kamsing Nonlaopon |
| author_facet | Meshari Alesemi Jameelah S. Al Shahrani Naveed Iqbal Rasool Shah Kamsing Nonlaopon |
| author_sort | Meshari Alesemi |
| collection | DOAJ |
| description | The exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept, we used the decomposition method along with natural transformation to discover the solution to a system of fractional-order partial differential equations. Using certain examples, the efficacy of the proposed technique is demonstrated. The exact and approximate solutions were shown to be in close contact in the graphical representation of the obtained results. We also examine whether the proposed method can achieve a quick convergence with a minimal number of calculations. The present approaches are also used to calculate solutions in various fractional orders. It has been proven that fractional-order solutions converge to integer-order solutions to problems. The current technique can be modified for various fractional-order problems due to its simple and straightforward implementation. |
| first_indexed | 2024-03-09T11:07:42Z |
| format | Article |
| id | doaj.art-ff9f9e510ca24b8698f7a8628fc5b090 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:07:42Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
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| series | Symmetry |
| spelling | doaj.art-ff9f9e510ca24b8698f7a8628fc5b0902023-12-01T00:53:52ZengMDPI AGSymmetry2073-89942023-01-0115123310.3390/sym15010233Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel OperatorsMeshari Alesemi0Jameelah S. Al Shahrani1Naveed Iqbal2Rasool Shah3Kamsing Nonlaopon4Department of Mathematics, College of Science, University of Bisha, Bisha 61922, Saudi ArabiaMathematics Department, College of Science, University of Bisha, P.O. Box 344, Bisha 61922, Saudi ArabiaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandThe exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept, we used the decomposition method along with natural transformation to discover the solution to a system of fractional-order partial differential equations. Using certain examples, the efficacy of the proposed technique is demonstrated. The exact and approximate solutions were shown to be in close contact in the graphical representation of the obtained results. We also examine whether the proposed method can achieve a quick convergence with a minimal number of calculations. The present approaches are also used to calculate solutions in various fractional orders. It has been proven that fractional-order solutions converge to integer-order solutions to problems. The current technique can be modified for various fractional-order problems due to its simple and straightforward implementation.https://www.mdpi.com/2073-8994/15/1/233Adomian decomposition methodnatural transformCaputo–Fabrizio (CF) and Atangana–Baleanu Caputo operator (ABC)fractional-order coupled systems |
| spellingShingle | Meshari Alesemi Jameelah S. Al Shahrani Naveed Iqbal Rasool Shah Kamsing Nonlaopon Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators Symmetry Adomian decomposition method natural transform Caputo–Fabrizio (CF) and Atangana–Baleanu Caputo operator (ABC) fractional-order coupled systems |
| title | Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators |
| title_full | Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators |
| title_fullStr | Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators |
| title_full_unstemmed | Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators |
| title_short | Analysis and Numerical Simulation of System of Fractional Partial Differential Equations with Non-Singular Kernel Operators |
| title_sort | analysis and numerical simulation of system of fractional partial differential equations with non singular kernel operators |
| topic | Adomian decomposition method natural transform Caputo–Fabrizio (CF) and Atangana–Baleanu Caputo operator (ABC) fractional-order coupled systems |
| url | https://www.mdpi.com/2073-8994/15/1/233 |
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