A Fractional Analysis of Zakharov–Kuznetsov Equations with the Liouville–Caputo Operator

In this study, we used two unique approaches, namely the Yang transform decomposition method (YTDM) and homotopy perturbation (HPTM), to derive approximate analytical solutions for nonlinear time-fractional Zakharov–Kuznetsov equations (ZKEs). This framework demonstrated behavior of weakly ion-acoustic waves in plasma containing cold ions hot isothermal electrons presence a uniform magnetic flux. The density fraction obliqueness compressive rarefactive potentials are depicted. Liouville–Caputo sense, fractional derivative is described. these procedures, first simplify problems then applied methods obtain comprehensive results problems. also made clear connections between precise issues under study. Illustrations reliability proposed techniques provided. clarified through graphs tables. procedures by illustrative examples. approaches attractive, though easy may be time-consuming solving diverse fractional-order partial differential equations.