Two-dimensional Legendre wavelet method for travelling wave solutions of time-fractional generalized seventh order KdV equation

[1]  Alfred Ramani,et al.  Structural stability of the Korteweg-De Vries solitons under a singular perturbation , 1988 .

[2]  Wen-Xiu Ma,et al.  Travelling wave solutions to a seventh order generalized KdV equation , 1993 .

[3]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[4]  D. Newland.  Wavelet Analysis of Vibration: Part 1—Theory , 1994 .

[5]  D. Newland.  Wavelet Analysis of Vibration: Part 2—Wavelet Maps , 1994 .

[6]  E. J. Parkes,et al.  Travelling solitary wave solutions to a seventh-order generalized KdV equation , 1996 .

[7]  B. Basu,et al.  SEISMIC RESPONSE OF SDOF SYSTEMS BY WAVELET MODELING OF NONSTATIONARY PROCESSES , 1998 .

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

[9]  B. Basu,et al.  On equivalent linearization using wavelet transform , 1999 .

[10]  Mohsen Razzaghi,et al.  THE LEGENDRE WAVELETS OPERATIONAL MATRIX OF INTEGRATION , 2001 .

[11]  Shijun Liao,et al.  On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..

[12]  M. Noor,et al.  Traveling Wave Solutions of Seventh-order Generalized KdV Equations Using He's Polynomials , 2009 .

[13]  Muhammad Aslam Noor,et al.  TRAVELING WAVE SOLUTIONS OF SEVENTH-ORDER GENERALIZED KdV EQUATIONS BY VARIATIONAL ITERATION METHOD USING ADOMIAN'S POLYNOMIALS , 2009 .

[14]  En-Bing Lin,et al.  Legendre wavelet method for numerical solutions of partial differential equations , 2010 .

[15]  Alvaro H. Salas,et al.  Application of the Cole-Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh-Order KdV Equation , 2010 .

[16]  S. Liao.  An optimal homotopy-analysis approach for strongly nonlinear differential equations , 2010 .

[17]  Rahmat Ali Khan,et al.  The Legendre wavelet method for solving fractional differential equations , 2011 .

[18]  Muhammad Aslam Noor,et al.  Modified Variational Iteration Method for Traveling Wave Solutions of Seventh-order Generalized KdV Equations , 2011 .

[19]  A. Gupta,et al.  Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena , 2014 .

[20]  A. Gupta,et al.  A two-dimensional Haar wavelet approach for the numerical simulations of time and space fractional Fokker–Planck equations in modelling of anomalous diffusion systems , 2014, Journal of Mathematical Chemistry.

[21]  Gui-qiong Xu,et al.  The integrability for a generalized seventh-order KdV equation: Painlevé property, soliton solutions, Lax pairs and conservation laws , 2014 .

[22]  A. K. Gupta,et al.  An investigation with Hermite Wavelets for accurate solution of Fractional Jaulent-Miodek equation associated with energy-dependent Schrödinger potential , 2015, Appl. Math. Comput..

[23]  A. K. Gupta,et al.  Numerical treatment for the solution of fractional fifth-order Sawada–Kotera equation using second kind Chebyshev wavelet method , 2015 .

[24]  A. K. Gupta,et al.  Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method , 2016 .

[25]  A. K. Gupta,et al.  The comparison of two reliable methods for accurate solution of time‐fractional Kaup–Kupershmidt equation arising in capillary gravity waves , 2016 .