New solutions of multidimensional fuzzy fractional coupled Burgers systems via He Laplace Carson algorithm.

The coupled Burgers model, a system of nonlinear partial differential equations, is widely used to describe complex interactions in various fields, including fluid dynamics, traffic flow, and biological systems. It provides insights into phenomena such as shock waves, turbulence, pattern formation, and transitions from order to chaos. This study applies the He-Laplace-Carson (HLC) scheme to solve the (3 + 1) dimensional coupled Burgers model under fuzzy-fractional conditions. The HLC scheme, which combines the homotopy perturbation method with the Laplace-Carson transform, is utilized to obtain accurate numerical solutions for these highly nonlinear systems. The model is analyzed in both fractional and fuzzy-fractional frameworks, enabling a comprehensive examination across lower and upper bounds, as well as the traditional crisp case. Two benchmark problems are investigated to evaluate the influence of Caputo fractional derivatives, with residual error analysis validating the accuracy of the results. Detailed two and three-dimensional visualizations, along with innovative contour plots, provide deeper physical interpretations of the model’s behavior. The findings demonstrate the robustness and effectiveness of the proposed methodology in addressing complex mathematical models that arise in diverse scientific applications.