LIE SYMMETRY, CONVERGENCE ANALYSIS, EXPLICIT SOLUTIONS, AND CONSERVATION LAWS FOR THE TIME-FRACTIONAL MODIFIED BENJAMIN-BONA-MAHONY EQUATION

Lie symmetry analysis is considered as one of the most powerful techniques that has been used for analyzing and extracting various types of solutions to partial differential equations. Conservation laws reflect important aspects of the behavior and properties of physical systems. This paper focuses on the investigation of the (1 + l)-dimensional time-fractional modified Benjamin-Bona-Mahony equation (mBBM) incorpomting Riemann-Liouville derivatives (RLD). Through the application of Lie sym¬metry analysis, the study explores similarity reductions and transforms the problem into a nonlinear ordinary differential equation with fractional order. A power series solution is obtained using the Erdelyi-Kober fractional operator, and the convergence of the solutions is analyzed. Furthermore, novel conservation laws for the time-fractional mBBM equation are established. The findings of the current work contribute to a deeper understanding of the dynamics of this fractional evolution equation and provide valuable insights into its behavior.