Exact Solutions For Fractional Differential Equations Arising in the Teaching of Mathematical Physical Equations By The Improved (G’/G) Method

  • Bin Zheng Shandong University of Technology
  • Qinghua Feng Shandong University of Technology
Keywords: Improved (G’/G) method, Fractional differential equations, Exact solutions, Fractional complex transformation, (2 1)-dimensional space-time fractional Nizhnik-Novikov-Veselov System


In this paper, we are concerned with seeking exact solutions for space-time fractional
differential equations arising in the teaching of the college course mathematical physical equations.
The improved (G’/G) method is extended to seek exact solutions for fractional differential equations
in the sense of the conformable fractional derivative. Based on a fractional complex transformation,
a certain fractional differential equation can be converted into another ordinary differential equation
of integer order, and then can be solved subsequently based on the homogeneous balance principle.
As for applications of this method, we apply it to solve the (2+1)-dimensional space-time fractional
Nizhnik-Novikov-Veselov System, and as a result, construct some new exact solutions for it.


Download data is not yet available.

Author Biographies

Bin Zheng, Shandong University of Technology

Shandong University of Technology
School of Mathematics and Statistics
Zhangzhou Road 12, Zibo, 255049, China

Qinghua Feng, Shandong University of Technology

Shandong University of Technology
School of Mathematics and Statistics
Zhangzhou Road 12, Zibo, 255049, China


[1] Q. Feng, Jacobi Elliptic Function Solutions For Fractional Partial Differential Equations, IAENG
International Journal of Applied Mathematics, 46(1)(2016), 121-129.
[2] S. Zhang and H.Q. Zhang, Fractional sub-equation method and its applications to nonlinear fractional
PDEs, Phys. Lett. A, 375(2011), 1069-1073.
[3] I. Aslan, Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Type- ˙
s, Commun. Theor. Phys. 65(2016), 39-45.
[4] Q. Feng and F. Meng, Explicit solutions for space-time fractional partial differential equations in
mathematical physics by a new generalized fractional Jacobi elliptic equation-based sub-equation
method, Optik 127(2016), 7450-7458.
[5] O. Acan, O. Firat, Y. Keskin and G. Oturanc, Conformable variational iteration method, New
Trends in Math. Sci. 5(1)(2017), 172-178.
[6] M. Yavuz and B. Ya¸skıran, Approximate-analytical solutions of cable equation using conformable
fractional operator, New Trends in Math. Sci. 5(4)(2017), 209-219.
[7] A.M.A. El-Sayed, S.H. Behiry and W.E. Raslan, Adomian’s decomposition method for solving an
intermediate fractional advection-dispersion equation, Comput. Math. Appl., 59(2010), 1759-1765.
[8] S. Guo, L. Mei and Y. Li, Fractional variational homotopy perturbation iteration method and its
application to a fractional diffusion equation, Appl. Math. Comput., 219(2013), 5909-5917.
[9] J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg. 178(1999), 257-
[10] J.H. He, A coupling method of homotopy technique and a perturbation technique for non-linear
problems, Inter. J. Non-Linear Mech. 35(2000), 37-43.
[11] T. Islam, M. Ali Akbar and A. K. Azad, Traveling wave solutions to some nonlinear fractional partial
differential equations through the rational (G’/G)-expansion method, J. Ocean Engi. Sci. 3(2018),
[12] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J.
Comput. Appl. Math. 264(2014), 65-70.
[13] B. Zheng, Exact Solutions for Some Fractional Partial Differential Equations by the (G’/G) Method,
Math. Pro. Engi. 2013, article ID: 826369(2013), 1-13.
[14] E. M. E. Zayed, The (G’/G)-expansion method and its applications to some nonlinear evolution
equations in the mathematical physics, J. Appl. Math. Computing, 30(2009), 89-103.