Variational principle, Hamiltonian and exact solutions of the fractional stochastic Nizhnik–Novikov–Veselov system

Purpose This study aims to investigate the stochastic Nizhnik–Novikov–Veselov (SNNV) system; incorporating local fractional derivatives, to enhance the understanding of its dynamics. Design/methodology/approach We utilize the semi-inverse method to formulate the variational principle, which serves as the foundation for deriving the Hamiltonian. To find various exact solutions of the fractional stochastic system, we propose a novel variable coefficient sub-equation method, which differs from traditional sub-equation methods that employ constant coefficients. Findings The proposed technique provides new analytical solutions, thereby enhancing our understanding of the system's dynamics. It establishes a robust framework for exploring similar fractional stochastic models in mathematical physics. Additionally, graphical simulations are presented to illustrate the physical relevance and behavior of the obtained solutions. Originality/value This study introduces a novel approach to solving fractional stochastic systems, contributing significant analytical tools and insights that advance the field of mathematical physics. Furthermore, we present a fractional and stochastic formulation of the SNNV system.