Soliton solution of fractional-order nonlinear differential equations based on the exp-function method

Abstract The exp-function method and fractional complex transform are applied for exact solutions of time fractional modified nonlinear Kawahara equation and fractional advection–diffusion-reaction equation with the modified Riemann–Liouville derivative. We see that this method is computationally applicable and effective.

[1]  Y. Khan,et al.  Exp‐function method for solitary and periodic solutions of Fitzhugh‐Nagumo equation , 2012 .

[2]  Adem C. Cevikel,et al.  Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations , 2013 .

[3]  Khaled A. Gepreel,et al.  Exact solutions for nonlinear partial fractional differential equations , 2012 .

[4]  E. Misirli,et al.  The modified Kudryashov method for solving some fractional-order nonlinear equations , 2014 .

[5]  Y. A. Amer,et al.  The first integral method and its application for finding the exact solutions of nonlinear fractional partial differential equations (PDES) in the mathematical physics , 2014 .

[6]  B. Zheng.  Exp-Function Method for Solving Fractional Partial Differential Equations , 2013, TheScientificWorldJournal.

[7]  M. Mirzazadeh,et al.  Application of first integral method to fractional partial differential equations , 2014 .

[8]  Ahmet Bekir,et al.  Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method , 2013 .

[9]  Dumitru Baleanu,et al.  On nonlinear fractional Klein-Gordon equation , 2011, Signal Process..

[10]  Liquan Mei,et al.  The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics ✩ , 2012 .

[11]  Y. Pandır,et al.  New Exact Solutions of the Time-Fractional Nonlinear Dispersive KdV Equation , 2013 .

[12]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[13]  R. Sahadevan,et al.  On solutions of two coupled fractional time derivative Hirota equations , 2014 .

[14]  ANJAN BISWAS,et al.  Solitons and periodic solutions to a couple of fractional nonlinear evolution equations , 2014 .

[15]  I. Podlubny.  Fractional differential equations , 1998 .

[16]  Ozkan Guner,et al.  Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods , 2014 .

[17]  Ji-Huan He,et al.  Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus , 2012 .

[18]  B. Zheng.  Exact Solutions for Some Fractional Partial Differential Equations by the Method , 2013 .

[19]  B. Lu.  The first integral method for some time fractional differential equations , 2012 .

[20]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[21]  K. Vishal,et al.  Application of homotopy analysis method for fractional Swift Hohenberg equation – Revisited , 2012 .

[22]  Hang Xu,et al.  Analysis of a time fractional wave-like equation with the homotopy analysis method , 2008 .

[23]  M. Dehghan,et al.  Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics , 2011 .

[24]  O. Kolebaje,et al.  Assessment of the Exact Solutions of the Space and Time Fractional Benjamin-Bona-Mahony Equation via the -Expansion Method, Modified Simple Equation Method, and Liu’s Theorem , 2014 .

[25]  New iteration methods for time fractional modified nonlinear kawahara equation , 2014 .

[26]  Dumitru Baleanu,et al.  On exact solutions of a class of fractional Euler–Lagrange equations , 2007, 0708.1433.

[27]  Guy Jumarie,et al.  Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions , 2009, Appl. Math. Lett..

[28]  Qi Wang,et al.  Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method , 2006, Appl. Math. Comput..

[29]  Roberto Garrappa,et al.  Exponential integrators for time–fractional partial differential equations , 2013 .

[30]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[31]  G. Jumarie,et al.  Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results , 2006, Comput. Math. Appl..

[32]  Adem C. Cevikel,et al.  A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations , 2014, TheScientificWorldJournal.

[33]  Adem C. Cevikel,et al.  Soliton solutions of (2+1)-dimensional time-fractional Zoomeron equation , 2016 .

[34]  Hong-qing Zhang,et al.  Fractional sub-equation method and its applications to nonlinear fractional PDEs , 2011 .

[35]  M. Kaplan,et al.  Exponential rational function method for space–time fractional differential equations , 2016 .

[36]  Hasan Bulut,et al.  The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation , 2013 .