Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel
This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation meth...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/4/615 |
| _version_ | 1797478336704806912 |
|---|---|
| author | Meshari Alesemi Naveed Iqbal Thongchai Botmart |
| author_facet | Meshari Alesemi Naveed Iqbal Thongchai Botmart |
| author_sort | Meshari Alesemi |
| collection | DOAJ |
| description | This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and the variational iterative transformation method in the sense of Caputo–Fabrizio. A numerical simulation was carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches are effective and efficient in investigating complicated non-linear models. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a very useful way, and this provides us with a simple process to adjust and control the convergence regions of the series solution. |
| first_indexed | 2024-03-09T21:30:28Z |
| format | Article |
| id | doaj.art-6954a7b3e1944031ad870d8af77b28ca |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:28Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6954a7b3e1944031ad870d8af77b28ca2023-11-23T20:57:30ZengMDPI AGMathematics2227-73902022-02-0110461510.3390/math10040615Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay KernelMeshari Alesemi0Naveed Iqbal1Thongchai Botmart2Department of Mathematics, College of Science, University of Bisha, P.O. Box 511, Bisha 61922, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandThis article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and the variational iterative transformation method in the sense of Caputo–Fabrizio. A numerical simulation was carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches are effective and efficient in investigating complicated non-linear models. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a very useful way, and this provides us with a simple process to adjust and control the convergence regions of the series solution.https://www.mdpi.com/2227-7390/10/4/615variational iterative methodCaputo–Fabrizio derivativeYang transformhomotopy perturbation methodpolytropic gas equation |
| spellingShingle | Meshari Alesemi Naveed Iqbal Thongchai Botmart Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel Mathematics variational iterative method Caputo–Fabrizio derivative Yang transform homotopy perturbation method polytropic gas equation |
| title | Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel |
| title_full | Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel |
| title_fullStr | Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel |
| title_full_unstemmed | Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel |
| title_short | Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel |
| title_sort | novel analysis of the fractional order system of non linear partial differential equations with the exponential decay kernel |
| topic | variational iterative method Caputo–Fabrizio derivative Yang transform homotopy perturbation method polytropic gas equation |
| url | https://www.mdpi.com/2227-7390/10/4/615 |
| work_keys_str_mv | AT mesharialesemi novelanalysisofthefractionalordersystemofnonlinearpartialdifferentialequationswiththeexponentialdecaykernel AT naveediqbal novelanalysisofthefractionalordersystemofnonlinearpartialdifferentialequationswiththeexponentialdecaykernel AT thongchaibotmart novelanalysisofthefractionalordersystemofnonlinearpartialdifferentialequationswiththeexponentialdecaykernel |