Improved fractional sub-equation method for (3+1) -dimensional generalized fractional KdV–Zakharov–Kuznetsov equations

• Published in: Computers & mathematics with applications (1987) Vol. 70; no. 2; pp. 158 - 166
• Main Authors: Sahoo, S., Saha Ray, S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2015
• Subjects: Construction; Derivatives; Exact solutions; Improved fractional sub-equation method; Mathematical analysis; Mathematical models; Mittag-Leffler function; Modified Riemann–Liouville derivative; Nonlinear evolution equations; space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation; Time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation; Improved fractional sub-equation method; Modified Riemann–Liouville derivative; space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation; Time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation; Mittag-Leffler function
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2015.05.002

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics, namely the time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) and space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equations by using improved fractional sub equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie’s modified Riemann–Liouville sense.