Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation
In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative. With the help of the obtained Lie point symmetries, the equation is reduced to nonlinear fractional...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2023/8241804 |
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| _version_ | 1832547887187230720 |
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| author | Maria Ihsane El Bahi Khalid Hilal |
| author_facet | Maria Ihsane El Bahi Khalid Hilal |
| author_sort | Maria Ihsane El Bahi |
| collection | DOAJ |
| description | In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative. With the help of the obtained Lie point symmetries, the equation is reduced to nonlinear fractional ordinary differential equations (NLFODEs) which contain the Erdélyi–Kober fractional differential operator. The equation is also studied by applying the power series method, which enables us to obtain extra solutions. The obtained power series solution is further examined for convergence. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators. |
| format | Article |
| id | doaj-art-f35ea41e3f284cb8b3d49594cd9cd6b7 |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-f35ea41e3f284cb8b3d49594cd9cd6b72025-02-03T06:43:03ZengWileyInternational Journal of Differential Equations1687-96512023-01-01202310.1155/2023/8241804Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage EquationMaria Ihsane El Bahi0Khalid Hilal1Sultan Moulay Slimane UniversitySultan Moulay Slimane UniversityIn this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative. With the help of the obtained Lie point symmetries, the equation is reduced to nonlinear fractional ordinary differential equations (NLFODEs) which contain the Erdélyi–Kober fractional differential operator. The equation is also studied by applying the power series method, which enables us to obtain extra solutions. The obtained power series solution is further examined for convergence. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.http://dx.doi.org/10.1155/2023/8241804 |
| spellingShingle | Maria Ihsane El Bahi Khalid Hilal Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation International Journal of Differential Equations |
| title | Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation |
| title_full | Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation |
| title_fullStr | Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation |
| title_full_unstemmed | Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation |
| title_short | Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation |
| title_sort | group analysis explicit power series solutions and conservation laws of the time fractional generalized foam drainage equation |
| url | http://dx.doi.org/10.1155/2023/8241804 |
| work_keys_str_mv | AT mariaihsaneelbahi groupanalysisexplicitpowerseriessolutionsandconservationlawsofthetimefractionalgeneralizedfoamdrainageequation AT khalidhilal groupanalysisexplicitpowerseriessolutionsandconservationlawsofthetimefractionalgeneralizedfoamdrainageequation |