The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives
Abstract In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02553-9 |
| _version_ | 1828173819258339328 |
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| author | Mohamed S. Abdel Latif Abass H. Abdel Kader Dumitru Baleanu |
| author_facet | Mohamed S. Abdel Latif Abass H. Abdel Kader Dumitru Baleanu |
| author_sort | Mohamed S. Abdel Latif |
| collection | DOAJ |
| description | Abstract In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter–Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman–Broer–Kaup-type equation, and a system of time fractional diffusion equations. |
| first_indexed | 2024-04-12T04:01:35Z |
| format | Article |
| id | doaj.art-413b09ebbe4b475399c32120bdded540 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-12T04:01:35Z |
| publishDate | 2020-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-413b09ebbe4b475399c32120bdded5402022-12-22T03:48:42ZengSpringerOpenAdvances in Difference Equations1687-18472020-03-012020111310.1186/s13662-020-02553-9The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivativesMohamed S. Abdel Latif0Abass H. Abdel Kader1Dumitru Baleanu2Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura UniversityMathematics and Engineering Physics Department, Faculty of Engineering, Mansoura UniversityDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya UniversityAbstract In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter–Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman–Broer–Kaup-type equation, and a system of time fractional diffusion equations.http://link.springer.com/article/10.1186/s13662-020-02553-9Fractional differential equationsGeneralized fractional derivativeInvariant subspace method |
| spellingShingle | Mohamed S. Abdel Latif Abass H. Abdel Kader Dumitru Baleanu The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives Advances in Difference Equations Fractional differential equations Generalized fractional derivative Invariant subspace method |
| title | The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives |
| title_full | The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives |
| title_fullStr | The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives |
| title_full_unstemmed | The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives |
| title_short | The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives |
| title_sort | invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives |
| topic | Fractional differential equations Generalized fractional derivative Invariant subspace method |
| url | http://link.springer.com/article/10.1186/s13662-020-02553-9 |
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