Lie symmetry analysis and exact solution of (2+1)-dimensional nonlinear time-fractional differential-difference equations

The invariant analysis of time-fractional nonlinear differential-difference equations and determination of their exact solutions using the Lie symmetry method is not discussed in the literature. In this paper, we present a systematic method to derive Lie point symmetries to nonlinear time-fractional differential-difference equations and illustrate its applicability through the physically important class of ( 2 + 1 )-dimensional time-fractional Toda lattice equations with Riemann–Liouville fractional derivative. We have shown the similarity reduction of the time-fractional nonlinear partial differential-difference equation into nonlinear fractional ordinary differential-difference equation in Erdélyi-Kober fractional derivative with a new independent variable. We derive their new exact solutions wherever possible utilising the Lie point symmetries. Our study reveals that the ( 2 + 1 )-dimensional nonlinear time-fractional Toda lattice equations admit the infinite-dimensional symmetry algebra.