A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations
In this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-12-01
|
| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2017-0145 |
| _version_ | 1818362648926879744 |
|---|---|
| author | Abdelrahman Mahmoud A.E. |
| author_facet | Abdelrahman Mahmoud A.E. |
| author_sort | Abdelrahman Mahmoud A.E. |
| collection | DOAJ |
| description | In this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system. |
| first_indexed | 2024-12-13T21:35:56Z |
| format | Article |
| id | doaj.art-ec25ea6bb7094930919bd320a2b85c78 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-13T21:35:56Z |
| publishDate | 2018-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-ec25ea6bb7094930919bd320a2b85c782022-12-21T23:30:42ZengDe GruyterNonlinear Engineering2192-80102192-80292018-12-017427928510.1515/nleng-2017-0145A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equationsAbdelrahman Mahmoud A.E.0Department of Mathematics, Faculty of Science, Mansoura University, 35516Mansoura, EgyptIn this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system.https://doi.org/10.1515/nleng-2017-0145modified riemann-liouville derivativericcati-bernoulli sub-ode methodexact solutionfractional zoomeron equation(3 + 1) dimensional space-time fractional mkdv-zk equation26a3334a0835a9935r1183c1565z05 |
| spellingShingle | Abdelrahman Mahmoud A.E. A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations Nonlinear Engineering modified riemann-liouville derivative riccati-bernoulli sub-ode method exact solution fractional zoomeron equation (3 + 1) dimensional space-time fractional mkdv-zk equation 26a33 34a08 35a99 35r11 83c15 65z05 |
| title | A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations |
| title_full | A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations |
| title_fullStr | A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations |
| title_full_unstemmed | A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations |
| title_short | A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations |
| title_sort | note on riccati bernoulli sub ode method combined with complex transform method applied to fractional differential equations |
| topic | modified riemann-liouville derivative riccati-bernoulli sub-ode method exact solution fractional zoomeron equation (3 + 1) dimensional space-time fractional mkdv-zk equation 26a33 34a08 35a99 35r11 83c15 65z05 |
| url | https://doi.org/10.1515/nleng-2017-0145 |
| work_keys_str_mv | AT abdelrahmanmahmoudae anoteonriccatibernoullisubodemethodcombinedwithcomplextransformmethodappliedtofractionaldifferentialequations AT abdelrahmanmahmoudae noteonriccatibernoullisubodemethodcombinedwithcomplextransformmethodappliedtofractionaldifferentialequations |