On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations
In this paper, we develop an analytical approximate solution for the nonlinear time-fractional Fisher’s equation using a right starting space function and a unique analytic-numeric technique referred to as the Laplace residual power series approach. The generalized Taylor’s formula and the Laplace t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/275 |
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| author | Rawya Al-deiakeh Sharifah Alhazmi Shrideh Al-Omari Mohammed Al-Smadi Shaher Momani |
| author_facet | Rawya Al-deiakeh Sharifah Alhazmi Shrideh Al-Omari Mohammed Al-Smadi Shaher Momani |
| author_sort | Rawya Al-deiakeh |
| collection | DOAJ |
| description | In this paper, we develop an analytical approximate solution for the nonlinear time-fractional Fisher’s equation using a right starting space function and a unique analytic-numeric technique referred to as the Laplace residual power series approach. The generalized Taylor’s formula and the Laplace transform operator are coupled in the aforementioned method, where the coefficients, obtained through fractional expansion in the Laplace space, are determined by applying the limit concept. In order to validate and illustrate the theoretical methodology of the LRPS technique, as well as to show its effectiveness, adaptability, and superiority in solving various types of nonlinear time and space fractional differential equations, numerical experiments are generated. The obtained analytical solutions are compatible with the precise solutions and concur with those proposed by the other approaches. The outcomes show that the Laplace residual power series strategy is incredibly successful, straightforward to implement, and well suited for handling the complexity of nonlinear problems. |
| format | Article |
| id | doaj-art-114fae13885e43768071b968b350e237 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-114fae13885e43768071b968b350e2372025-08-20T03:14:39ZengMDPI AGFractal and Fractional2504-31102025-04-019527510.3390/fractalfract9050275On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s EquationsRawya Al-deiakeh0Sharifah Alhazmi1Shrideh Al-Omari2Mohammed Al-Smadi3Shaher Momani4Department of Mathematics, Faculty of Science, Irbid National University, Irbid 21110, JordanDepartment of Mathematics, College of Education for Girls at Al-Qunfudah, Umm Al-Qura University, Mecca 11942, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanDepartment of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanNonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 20550, United Arab EmiratesIn this paper, we develop an analytical approximate solution for the nonlinear time-fractional Fisher’s equation using a right starting space function and a unique analytic-numeric technique referred to as the Laplace residual power series approach. The generalized Taylor’s formula and the Laplace transform operator are coupled in the aforementioned method, where the coefficients, obtained through fractional expansion in the Laplace space, are determined by applying the limit concept. In order to validate and illustrate the theoretical methodology of the LRPS technique, as well as to show its effectiveness, adaptability, and superiority in solving various types of nonlinear time and space fractional differential equations, numerical experiments are generated. The obtained analytical solutions are compatible with the precise solutions and concur with those proposed by the other approaches. The outcomes show that the Laplace residual power series strategy is incredibly successful, straightforward to implement, and well suited for handling the complexity of nonlinear problems.https://www.mdpi.com/2504-3110/9/5/275Caputo fractional derivativesFisher’s equationtime-fractional equationresidual power seriesLaplace residual power seriesfractional series expansion |
| spellingShingle | Rawya Al-deiakeh Sharifah Alhazmi Shrideh Al-Omari Mohammed Al-Smadi Shaher Momani On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations Fractal and Fractional Caputo fractional derivatives Fisher’s equation time-fractional equation residual power series Laplace residual power series fractional series expansion |
| title | On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations |
| title_full | On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations |
| title_fullStr | On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations |
| title_full_unstemmed | On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations |
| title_short | On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations |
| title_sort | on the laplace residual series method and its application to time fractional fisher s equations |
| topic | Caputo fractional derivatives Fisher’s equation time-fractional equation residual power series Laplace residual power series fractional series expansion |
| url | https://www.mdpi.com/2504-3110/9/5/275 |
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