The First Integral Method for the time fractional Kaup-Boussinesq System with time dependent coefficient

The first integral method (FIM) is applied to reach the different type solutions of the time fractional Kaup-Boussinesq (fKB) system with time dependent coefficient. It is obtained the envelope, bell shaped, triangular and kink soliton solutions of this equation. The method is an effective one to reach the different types of solutions of fractional nonlinear partial differential equations (fNPDE).

[1]  Guy Jumarie,et al.  Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order , 2010, Appl. Math. Lett..

[2]  B. M. Fulk MATH , 1992 .

[3]  A. Bekir,et al.  The First Integral Method for Exact Solutions of Nonlinear Fractional Differential Equations , 2015 .

[4]  Andrew G. Glen,et al.  APPL , 2001 .

[5]  Saeid Abbasbandy,et al.  The first integral method for modified Benjamin–Bona–Mahony equation , 2010 .

[6]  Ismail Aslan Travelling wave solutions to nonlinear physical models by means of the first integral method , 2011 .

[7]  C. M. Place,et al.  Ordinary Differential Equations , 1982 .

[8]  Zuntao Fu,et al.  New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations , 2001 .

[9]  R. Ansari,et al.  Exact solutions of some nonlinear systems of partial differential equations by using the first integral method , 2012 .

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

[11]  Min Chen,et al.  Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory , 2002, J. Nonlinear Sci..

[12]  C. M. Khalique,et al.  Dark solitons of the Biswas–Milovic equation by the first integral method , 2013 .

[13]  Xing-Biao Hu,et al.  Application of Hirota's bilinear formalism to the Toeplitz lattice—some special soliton-like solutions , 2002 .

[14]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[15]  A. Bekir,et al.  Analytic treatment of nonlinear evolution equations using first integral method , 2012 .

[16]  Sheng Zhang,et al.  Exp-function method for solving Maccari's system , 2007 .

[17]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[18]  P. Drazin,et al.  Solitons: An Introduction , 1989 .

[19]  Zhaosheng Feng,et al.  The first-integral method to study the Burgers–Korteweg–de Vries equation , 2002 .

[20]  K. R. Raslan The first integral method for solving some important nonlinear partial differential equations , 2008 .

[21]  Ahmet Bekir,et al.  Travelling wave solutions of the Cahn-Allen equation by using first integral method , 2009, Appl. Math. Comput..

[22]  P. Hartman Ordinary Differential Equations , 1965 .

[23]  Mingliang Wang,et al.  The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics , 2008 .

[24]  Guy Jumarie,et al.  Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution , 2007 .

[25]  Ji-Huan He,et al.  Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method , 2007, Comput. Math. Appl..

[26]  Zhang Hong-qing,et al.  New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation* , 2004 .