Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method
Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand the complexity of these phenomena. This article introduces a recent attractive analytic-numeric approach to investigate the approximate solutions for nonlinear time fractio...
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/1980 |
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| author | Hussam Aljarrah Mohammad Alaroud Anuar Ishak Maslina Darus |
| author_facet | Hussam Aljarrah Mohammad Alaroud Anuar Ishak Maslina Darus |
| author_sort | Hussam Aljarrah |
| collection | DOAJ |
| description | Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand the complexity of these phenomena. This article introduces a recent attractive analytic-numeric approach to investigate the approximate solutions for nonlinear time fractional partial differential equations by means of coupling the Laplace transform operator and the fractional Taylor’s formula. The validity and the applicability of the used method are illustrated via solving nonlinear time-fractional Kolmogorov and Rosenau–Hyman models with appropriate initial data. The approximate series solutions for both models are produced in a rapid convergence McLaurin series based upon the limit of the concept with fewer computations and more accuracy. Graphs in two and three dimensions are drawn to detect the effect of time-Caputo fractional derivatives on the behavior of the obtained results to the aforementioned models. Comparative results point out a more accurate approximation of the proposed method compared with existing methods such as the variational iteration method and the homotopy perturbation method. The obtained outcomes revealed that the proposed approach is a simple, applicable, and convenient scheme for solving and understanding a variety of non-linear physical models. |
| first_indexed | 2024-03-09T23:09:55Z |
| format | Article |
| id | doaj.art-8d40c5e66cbc4b7db67ce7aa962a5eb8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:09:55Z |
| publishDate | 2022-06-01 |
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| spelling | doaj.art-8d40c5e66cbc4b7db67ce7aa962a5eb82023-11-23T17:47:44ZengMDPI AGMathematics2227-73902022-06-011012198010.3390/math10121980Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series MethodHussam Aljarrah0Mohammad Alaroud1Anuar Ishak2Maslina Darus3Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, MalaysiaDepartment of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, JordanDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, MalaysiaMost physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand the complexity of these phenomena. This article introduces a recent attractive analytic-numeric approach to investigate the approximate solutions for nonlinear time fractional partial differential equations by means of coupling the Laplace transform operator and the fractional Taylor’s formula. The validity and the applicability of the used method are illustrated via solving nonlinear time-fractional Kolmogorov and Rosenau–Hyman models with appropriate initial data. The approximate series solutions for both models are produced in a rapid convergence McLaurin series based upon the limit of the concept with fewer computations and more accuracy. Graphs in two and three dimensions are drawn to detect the effect of time-Caputo fractional derivatives on the behavior of the obtained results to the aforementioned models. Comparative results point out a more accurate approximation of the proposed method compared with existing methods such as the variational iteration method and the homotopy perturbation method. The obtained outcomes revealed that the proposed approach is a simple, applicable, and convenient scheme for solving and understanding a variety of non-linear physical models.https://www.mdpi.com/2227-7390/10/12/1980Riemann–Liouville fractional integral operatorfractional partial differential equationsLaplace power series methodinverse Laplace transformtime-Caputo fractional derivative |
| spellingShingle | Hussam Aljarrah Mohammad Alaroud Anuar Ishak Maslina Darus Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method Mathematics Riemann–Liouville fractional integral operator fractional partial differential equations Laplace power series method inverse Laplace transform time-Caputo fractional derivative |
| title | Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method |
| title_full | Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method |
| title_fullStr | Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method |
| title_full_unstemmed | Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method |
| title_short | Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method |
| title_sort | approximate solution of nonlinear time fractional pdes by laplace residual power series method |
| topic | Riemann–Liouville fractional integral operator fractional partial differential equations Laplace power series method inverse Laplace transform time-Caputo fractional derivative |
| url | https://www.mdpi.com/2227-7390/10/12/1980 |
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