Abstract
In this paper, the improved fractional subequation method is applied to establish the exact solutions for some nonlinear fractional partial differential equations. Solutions to the generalized time fractional biological population model, the generalized time fractional compound KdV-Burgers equation, the space-time fractional regularized long-wave equation, and the (3+1)-space-time fractional Zakharov-Kuznetsov equation are obtained, respectively.
Highlights
Fractional differential equations are widely used to describe lots of important phenomena and dynamic processes in physics, engineering, electromagnetics, acoustics, viscoelasticity electrochemistry, material science, stochastic dynamical system, plasma physics, controlled thermonuclear fusion, nonlinear control theory, image processing, nonlinear biological systems and astrophysics, etc. [1,2,3,4,5,6,7]
We aim to find new exact solutions of some important partial fractional differential equations under Jumarie’s definition by improved fractional subequation method
Applying a suitable fractional complex transform of the improved fractional subequation method and the chain rule, nonlinear fractional differential equations with the modified Riemann-Liouville derivative can be converted into nonlinear ordinary differential equations
Summary
Fractional differential equations are widely used to describe lots of important phenomena and dynamic processes in physics, engineering, electromagnetics, acoustics, viscoelasticity electrochemistry, material science, stochastic dynamical system, plasma physics, controlled thermonuclear fusion, nonlinear control theory, image processing, nonlinear biological systems and astrophysics, etc. [1,2,3,4,5,6,7]. We introduce the aforementioned fractional partial differential equations They are the generalized time fractional biological population model, the generalized time fractional compound KdV-Burgers equation, the spacetime fractional regularized long-wave equation, and the (3 + 1)-space-time fractional Zakharov-Kuznetsov equation. The space-time fractional regularized long-wave equation is given by [41]: Dαt u + k1Dαx u + k2uDαx u + k3Dαt D2xαu = 0, ð13Þ where u = uðx, tÞ is an unknown function, Dαxu is the modified Riemann-Liouville derivative of order α for a function u, and D2xαu = Dαx ðDαx uÞ. Motivated by the above results, in this paper, we use the improved subequation method to find new exact solutions of the generalized time fractional biological population model, the generalized time fractional compound KdV-Burgers equation, the space-time fractional regularized long-wave equation, and the (3 + 1)-space-time fractional Zakharov-Kuznetsov equation, respectively
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
