Wave solutions in (3 + 1)-dimensional generalized fractional mKdV-ZK equation utilizing jacobi elliptic functions

Abstract

In this research, we investigate the e ects of fractional order on the (3 + 1)-dimensional general-
ized space-time fractional modi ed KdV-Zakharov-Kuznetsov (mKdV-ZK) equation. We approach
the problem by utilizing the conformable fractional derivative. By reducing the mKdV-ZK equation
to an integer order nonlinear ordinary di erential equation, we apply the Jacobi elliptic function
method to nd exact solutions. These solutions are speci cally tailored for the fractional order of
the (3 + 1)-dimensional generalized mKdV-ZK equation, encompassing solitary waves, shock waves,
and periodic waves. We also compare these exact solutions with fractional solutions to gain further
insights. Notably, our approach demonstrates the feasibility of solving nonlinear time-fractional
di erential equations with conformable derivatives. Several diagrams have been included to visually
depict the behavior of the solutions under fractional order when certain special parameter values
are employed.