Abstract. In this study, we revisit the stochastic potential-KdV equation by considering the time-derivative of Caputo-type and the time-coordinate to be affected by proportional delay. We apply two approaches namely, fractional Maclaurin series and novel Homotopy perturbation method, to construct closed-form solutions to the proposed model. A graphical scheme is conducted to study the simulations of fractional time-derivative against the proportional delay-time. Finally, we investigate the influence of the model’s coefficients on the propagation of the obtained solutions.

Key words: Stochastic potential-KdV; Caputo derivative; Fractional Maclaurin series; Homotopy perturbation method.