Articles written in Pramana – Journal of Physics

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


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      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 presenta 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-differenceequation 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.

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