<p>This paper presents new analytical solutions for the time-fractional Boiti-Leon-Manna-Pempinelli (BLMP) equation, a crucial model for physical phenomena. Our approach yields novel wave solutions, whose propagation and dynamics are examined for diverse parameter values. The obtained solutions contain rational and natural logarithm functions. The graphical representations of the attained solutions are represented by plotted graphs with suitable parameters. The plotted graphs show different solitons and nonlinear wave solutions. The examination of these solutions involves a comprehensive analysis of their propagation and dynamics through analytic techniques. Our results with existing literature and found that our approach yields more accurate and efficient solutions. The novelty of these solutions is essential for understanding nonlinear behavior and natural phenomena. By developing analytical methods for nonlinear equations, this work advances our knowledge of complex systems. The results provide valuable insights into the equation’s behavior, shedding light on the underlying physical mechanisms. This research contributes to the development of analytical methods for nonlinear equations, fostering future research in the field. The findings are relevant to various areas of physics, including wave dynamics and nonlinear systems.</p>