A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations

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...

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Main Author: Abdelrahman Mahmoud A.E.
Format: Article
Language:English
Published: De Gruyter 2018-12-01
Series:Nonlinear Engineering
Subjects:
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
Online Access:https://doi.org/10.1515/nleng-2017-0145
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spelling doaj-ec25ea6bb7094930919bd320a2b85c782021-09-06T19:21:07ZengDe 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
collection DOAJ
language English
format Article
sources DOAJ
author Abdelrahman Mahmoud A.E.
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
author_facet Abdelrahman Mahmoud A.E.
author_sort Abdelrahman Mahmoud A.E.
title 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_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_sort note on riccati-bernoulli sub-ode method combined with complex transform method applied to fractional differential equations
publisher De Gruyter
series Nonlinear Engineering
issn 2192-8010
2192-8029
publishDate 2018-12-01
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.
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
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