AbstractThis study investigates the application of the Elzaki Projected Differential Transform Method (EPDTM) to fractional-order nonlinear Korteweg-de Vries (KdV) equations, which describe various nonlinear wave phenomena in physics and engineering. The method effectively addresses both linear and nonlinear operators and fractional derivatives. Through two illustrative examples, the method accurately captures the dynamics of fractional-order wave systems and achieves results in excellent agreement with exact solutions. The findings demonstrate the method_s precision, fast convergence, and computational efficiency, underscoring EPDTM's potential as a robust tool for solving nonlinear partial differential equations with fractional dynamics.
Keywords Fractional Korteweg-de Vries equations, Elzaki transform, Projected Differential Transform Method, Fractional calculus, Numerical simulation..