New Analytical Solutions and Stability Analysis of Coupled Time-Fractional Boussinesq-Burgers System

This manuscript investigates a coupled time-fractional Boussinesq-Burgers system (CTFBBS) and presents new analytical solutions for the model. The exact solutions are obtained by employing the Exp$(-\Phi(\eta))$-expansion method combined with the fractional complex transformation. The obtained solution set includes different functional forms, such as hyperbolic and trigonometric solutions, demonstrating the effectiveness and versatility of the proposed analytical technique for nonlinear fractional partial differential equations.To support the analytical findings, numerical simulations based on a finite difference scheme are performed in order to validate the accuracy of the exact solutions. Furthermore, the stability characteristics of the considered system are investigated through linear stability analysis. Finally, the symbolic computation software \textit{Mathematica 11} is utilized to solve the resulting nonlinear algebraic system and to generate surface and contour plots illustrating some representative solutions of the model.