univ. j. math. appl. Universal Journal of Mathematics and Applications 2619-9653 Emrah Evren KARA 10.32323/ujma.1792704 Numerical and Computational Mathematics (Other) Partial Differential Equations Sayısal ve Hesaplamalı Matematik (Diğer) Kısmi Diferansiyel Denklemler New Analytical Solutions and Stability Analysis of Coupled Time-Fractional Boussinesq-Burgers System https://orcid.org/0009-0000-1845-6661 Cherief Rachid UNIVERSITY AHMED ZABANA OF RELIZANE https://orcid.org/0000-0002-4390-9404 Djilali Medjahed UNIVERSITY AHMED ZABANA OF RELIZANE https://orcid.org/0009-0004-3759-2211 Ould Melha Khellaf HASSIBA BENBOUALI UNIVERSITY https://orcid.org/0000-0002-4568-9732 Thabet Sabri T. M. SAVEETHA UNIVERSITY https://orcid.org/0000-0002-8889-3768 Abdeljawad Thabet PRINCE SULTAN UNIVERSITY Advanced Online Publication 09 30 2025 03 28 2026 Copyright © 2018, Universal Journal of Mathematics and Applications 2018 Universal Journal of Mathematics and Applications

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.

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