Articles written in Pramana – Journal of Physics
Volume 93 Issue 2 August 2019 Article ID 0021 Research Article
In this paper, the Lie group analysis method is applied to carry out the Lie point symmetries of some space–time fractional systems including coupled Burgers equations, Ito’s system, coupled Korteweg–de-Vries(KdV) equations, Hirota–Satsuma coupled KdV equations and coupled nonlinear Hirota equations with time-dependent variable coefficients with the Riemann–Liouville derivative. Symmetry reductions are constructed using Lie symmetries of the systems. To the best of our knowledge, nobody has so far derived the invariants of space–time nonlinear fractional partial differential equations with time-dependent coefficients.
Volume 95 All articles Published: 18 October 2021 Article ID 0176 Research Article
The objective of this manuscript is to analyse space–time fractional generalised Hirota–Satsuma coupled Korteweg–de Vries (HSCKdV) system with time-dependent variable coefficients for exact solution using power series method corresponding to Lie symmetry reduction of HSCKdV system. The exact solution obtained in power series form is further analysed for convergence. Conservation laws of the HSCKdV system are constructed by using the new conservation theorem and generalised fractional Noether’s operator.
Volume 95, 2021
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