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

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Abstract

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.

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Authors and Affiliations

  1. Indian Institute of Information Technology Kottayam, Valavoor, 686 635, India

    T Bakkyaraj & Reetha Thomas

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  1. T Bakkyaraj
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  2. Reetha Thomas
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Correspondence to T Bakkyaraj.

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Bakkyaraj, T., Thomas, R. Lie symmetry analysis and exact solution of \((2+1)\)-dimensional nonlinear time-fractional differential-difference equations. Pramana - J Phys 96, 225 (2022). https://doi.org/10.1007/s12043-022-02469-x

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  • DOI: https://doi.org/10.1007/s12043-022-02469-x

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