Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method
In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9179826 |
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| author | Haifa Bin Jebreen |
| author_facet | Haifa Bin Jebreen |
| author_sort | Haifa Bin Jebreen |
| collection | DOAJ |
| description | In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. Also, the fractional derivatives in the sense of β-derivative are defined. Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation β-derivative. These equations are analyzed utilizing an integration scheme, namely, the rational exp−Ωη-expansion method. Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so on. |
| format | Article |
| id | doaj-art-7426bd4179c0456298d6eafa9cfe0506 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-7426bd4179c0456298d6eafa9cfe05062025-02-03T05:53:22ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/91798269179826Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion MethodHaifa Bin Jebreen0Mathematics Department, College of Science, King Saud University, Riyadh, Saudi ArabiaIn this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. Also, the fractional derivatives in the sense of β-derivative are defined. Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation β-derivative. These equations are analyzed utilizing an integration scheme, namely, the rational exp−Ωη-expansion method. Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so on.http://dx.doi.org/10.1155/2020/9179826 |
| spellingShingle | Haifa Bin Jebreen Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method Complexity |
| title | Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method |
| title_full | Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method |
| title_fullStr | Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method |
| title_full_unstemmed | Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method |
| title_short | Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method |
| title_sort | some nonlinear fractional pdes involving β derivative by using rational exp ωη expansion method |
| url | http://dx.doi.org/10.1155/2020/9179826 |
| work_keys_str_mv | AT haifabinjebreen somenonlinearfractionalpdesinvolvingbderivativebyusingrationalexpōēexpansionmethod |