This research study aims to determine a novel and modest algorithm for weak, nonlinear ion-acoustic waves in a highly magnetized, lossless plasma in 2 dimensions, namely the Zakharov-Kuznetsov equation, using the fractional reduced-differential transformation method (FRDTM). This approach is an advanced modification of the Laplace-transform algorithm to simplify the calculation. FRDTM has to establish the analytical solution or closed numerical solution for any kind of ordinary, partial and fractional differential equations. Numerical results, accompanied by graphical demonstrations, show that the proposed approach provides reliable, accurate results and offers a new explanation for a different type of dynamical system.
Keywords: Fractional calculus, Approximate solution, Zakharov-Kuznetsov equation, Non-linear fractional, fractional differential equations, reduced differential transformation method (RDTM)
Published by Breakthrough: A Multidisciplinary Journal. Publication date: May 6, 2026. DOI: 10.58517/BAMJ.2026.111.