Lie symmetry analysis and exact solutions of conformable time-space fractional Benjamin-Bona-Mahony equations
Keywords:
Benjamin-Bona-Mahony equation, Lie symmetry analysis, (G′/G)-expansion technique, Conformable fractional derivative, Bifurcation analysisAbstract
This article investigates the invariance properties of nonlinear fractional partial differential equations involving conformable fractional derivatives in both time and space through the framework of Lie symmetry analysis. The study focuses on three significant forms of the Benjamin-Bona-Mahony (BBM) equations. The corresponding Lie symmetry generators and vector fields are systematically derived and employed to reduce the governing equations to ordinary differential equations. Exact analytical solutions are then constructed by utilising the (G'/G) -expansion method for the time-space fractional BBM equation. At the same time, suitable ansatz-based techniques are adopted to obtain explicit solutions for the modified and power-law fractional BBM equations. Furthermore, a qualitative dynamical analysis is carried out for the time-space fractional BBM equation and its modified form using bifurcation analysis and phase portraits, which reveal the behaviour of solution trajectories near the critical equilibrium points and provide insight into the nonlinear dynamics of the considered models. The results demonstrate that combining Lie symmetry analysis with analytical solution techniques provides an effective, systematic approach to studying nonlinear fractional BBM-type equations and deepens understanding of their mathematical structure and physical characteristics.
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Copyright (c) 2026 Amit, Rajeev Kumar, Anupma Bansal, Abdallah M. Talafha, Sandeep Malik
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