Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/a-note-on-riccati-bernoulli-sub-ode-method-combined-with-complex-wl0bUjbCy3
References (40)
-
Bo Tang, Yinnian He, Leilei Wei, Xindong Zhang (2012)
A generalized fractional sub-equation method for fractional differential equations with variable coefficients☆Physics Letters A, 376
-
Sheng Zhang, Hong-qing Zhang (2011)
Fractional sub-equation method and its applications to nonlinear fractional PDEsPhysics Letters A, 375
-
F. Demontis (2010)
Exact solutions of the modified Korteweg-de Vries equationTheoretical and Mathematical Physics, 168
-
(2012)
The rst integral method for some time fractional differential equations -
Zheng Bin (2012)
（G＇/G）-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical PhysicsCommunications in Theoretical Physics, 58
-
M. Alquran, Kamel Al-khaled (2012)
Mathematical methods for a reliable treatment of the (2+1)-dimensional Zoomeron equationMathematical Sciences, 6
-
(2006)
Theory and Applications of Fractional Di erential Equations -
B. Zheng (2011)
A NEW BERNOULLI SUB-ODE METHOD FOR CONSTRUCTING TRAVELING WAVE SOLUTIONS FOR TWO NONLINEAR EQUATIONS WITH ANY ORDER -
Exact solutions of the modi ed Korteweg – de Vries , Theoret -
M. Inc., A. Aliyu, A. Yusuf (2017)
Traveling wave solutions and conservation laws of some fifth-order nonlinear equationsThe European Physical Journal Plus, 132
-
郑滨 (2012)
(G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics -
G. Jumarie (2006)
Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further resultsComput. Math. Appl., 51
-
(2013)
Exact Solutions for Three Fractional Partial Differential Equations by the G ′G $\begin{array}{} \displaystyle \frac{G^{\,\,\prime}}{G} \end{array}$ Method -
S. Samko, A. Kilbas, O. Marichev (1993)
Fractional Integrals and Derivatives: Theory and Applications -
Feng Xu (2013)
A Generalized Sub-ODE Method and Applications for Nonlinear Evolution EquationsJournal of Scientific Research and Reports, 2
-
Z. Ganji, D. Ganji, Y. Rostamiyan (2009)
Solitary wave solutions for a time-fraction generalized Hirota–Satsuma coupled KdV equation by an analytical techniqueApplied Mathematical Modelling, 33
-
(1993)
Riemann – Liouville derivative and fractional Taylor series of nondi erentiable functions further results -
Wenjun Liu, Kewang Chen (2013)
The functional variable method for finding exact solutions of some nonlinear time-fractional differential equationsPramana, 81
-
K. Miller, Bertram Ross (1993)
An Introduction to the Fractional Calculus and Fractional Differential Equations -
Ozkan Guner, E. Aksoy, A. Bekir, A. Cevikel (2016)
Different methods for (3+1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equationComput. Math. Appl., 71
-
S. Ege, E. Mısırlı (2014)
The modified Kudryashov method for solving some fractional-order nonlinear equationsAdvances in Difference Equations, 2014
-
B. Lu (2012)
The first integral method for some time fractional differential equationsJournal of Mathematical Analysis and Applications, 395
-
Abdelrahman Mae, Sohalya Ma (2017)
Solitary Waves for the Modified Korteweg-De Vries Equation in Deterministic Case and Random CaseJournal of Physical Mathematics, 8
-
R. Mace, M. Hellberg (2001)
The Korteweg–de Vries–Zakharov–Kuznetsov equation for electron-acoustic wavesPhysics of Plasmas, 8
-
M. Caputo (1967)
Linear Models of Dissipation whose Q is almost Frequency Independent-IIGeophysical Journal International, 13
-
S. Sahoo, S. Ray (2015)
Improved fractional sub-equation method for (3+1) -dimensional generalized fractional KdV-Zakharov-Kuznetsov equationsComput. Math. Appl., 70
-
(2013)
Exact Solutions for Three Fractional Partial Di erential Equations by the ( G -
(2011)
Exact solutions of the modi ed Korteweg–de Vries -
A. Bekir, Ozkan Guner, A. Cevikel (2013)
Fractional Complex Transform and exp-Function Methods for Fractional Differential EquationsAbstract and Applied Analysis, 2013
-
(2016)
Di erent methods for (3+1)-dimensional space-time fractional modi ed KdV- Zakharov-Kuznetsov equation -
M. Abdelrahman, M. Sohaly (2017)
Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in the stochastic input caseThe European Physical Journal Plus, 132
-
(2010)
A generalized expfunction method for fractional riccati di erential equations -
Ismail Aslan (2014)
Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV EquationCommunications in Theoretical Physics, 61
-
(1999)
Fractional Di erential Equations -
Ji-Huan He, S. Elagan, Z. Li (2012)
Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculusPhysics Letters A, 376
-
S. Ray, S. Sahoo (2015)
A Novel Analytical Method with Fractional Complex Transform for New Exact Solutions of Time-Fractional Fifth-Order Sawada-Kotera EquationReports on Mathematical Physics, 75
-
G. Jumarie (2009)
Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functionsAppl. Math. Lett., 22
-
S. Zhang (2010)
A GENERALIZED EXP-FUNCTION METHOD FOR FRACTIONAL RICCATI DIFFERENTIAL EQUATIONS, 1
-
Xiao-Feng Yang, Z. Deng, Yi Wei (2015)
A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its applicationAdvances in Difference Equations, 2015
-
Ozkan Guner, A. Bekir, Halis Bilgil (2015)
A note on exp-function method combined with complex transform method applied to fractional differential equationsAdvances in Nonlinear Analysis, 4
- Publisher
- de Gruyter
- Copyright
- © 2018 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 2192-8029
- eISSN
- 2192-8029
- DOI
- 10.1515/nleng-2017-0145
- Publisher site
- See Article on Publisher Site
Abstract
AbstractIn 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.
Journal
Nonlinear Engineering – de Gruyter
Published: Dec 19, 2018