Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media
This paper investigates the fractional local Poisson equation using the homotopy perturbation transformation method. The Poisson equation discusses the potential area due to a provided charge with the possibility of area identified, and one can then determine the electrostatic or gravitational area...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1323 |
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| author | Manal Alqhtani Khaled M. Saad Rasool Shah Wajaree Weera Waleed M. Hamanah |
| author_facet | Manal Alqhtani Khaled M. Saad Rasool Shah Wajaree Weera Waleed M. Hamanah |
| author_sort | Manal Alqhtani |
| collection | DOAJ |
| description | This paper investigates the fractional local Poisson equation using the homotopy perturbation transformation method. The Poisson equation discusses the potential area due to a provided charge with the possibility of area identified, and one can then determine the electrostatic or gravitational area in the fractal domain. Elliptic partial differential equations are frequently used in the modeling of electromagnetic mechanisms. The Poisson equation is investigated in this work in the context of a fractional local derivative. To deal with the fractional local Poisson equation, some illustrative problems are discussed. The solution shows the well-organized and straightforward nature of the homotopy perturbation transformation method to handle partial differential equations having fractional derivatives in the presence of a fractional local derivative. The solutions obtained by the defined methods reveal that the proposed system is simple to apply, and the computational cost is very reliable. The result of the fractional local Poisson equation yields attractive outcomes, and the Poisson equation with a fractional local derivative yields improved physical consequences. |
| first_indexed | 2024-03-09T12:57:03Z |
| format | Article |
| id | doaj.art-8c23aaa4932348db87440c8c3bdb0d3d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:57:03Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8c23aaa4932348db87440c8c3bdb0d3d2023-11-30T21:59:31ZengMDPI AGSymmetry2073-89942022-06-01147132310.3390/sym14071323Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous MediaManal Alqhtani0Khaled M. Saad1Rasool Shah2Wajaree Weera3Waleed M. Hamanah4Department of Mathematics, College of Sciences and Arts, Najran University, Najran 11001, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, Najran University, Najran 11001, Saudi ArabiaDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandInterdisciplinary Research Center in Renewable Energy and Power Systems, King Fahd University for Petroleum and Minerals, Dhahran 31261, Saudi ArabiaThis paper investigates the fractional local Poisson equation using the homotopy perturbation transformation method. The Poisson equation discusses the potential area due to a provided charge with the possibility of area identified, and one can then determine the electrostatic or gravitational area in the fractal domain. Elliptic partial differential equations are frequently used in the modeling of electromagnetic mechanisms. The Poisson equation is investigated in this work in the context of a fractional local derivative. To deal with the fractional local Poisson equation, some illustrative problems are discussed. The solution shows the well-organized and straightforward nature of the homotopy perturbation transformation method to handle partial differential equations having fractional derivatives in the presence of a fractional local derivative. The solutions obtained by the defined methods reveal that the proposed system is simple to apply, and the computational cost is very reliable. The result of the fractional local Poisson equation yields attractive outcomes, and the Poisson equation with a fractional local derivative yields improved physical consequences.https://www.mdpi.com/2073-8994/14/7/1323homotopy perturbation transformation methodfractional local Poisson equationlocal Caputo operatorSumudu transform |
| spellingShingle | Manal Alqhtani Khaled M. Saad Rasool Shah Wajaree Weera Waleed M. Hamanah Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media Symmetry homotopy perturbation transformation method fractional local Poisson equation local Caputo operator Sumudu transform |
| title | Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media |
| title_full | Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media |
| title_fullStr | Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media |
| title_full_unstemmed | Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media |
| title_short | Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media |
| title_sort | analysis of the fractional order local poisson equation in fractal porous media |
| topic | homotopy perturbation transformation method fractional local Poisson equation local Caputo operator Sumudu transform |
| url | https://www.mdpi.com/2073-8994/14/7/1323 |
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