Lie Symmetry and Exact Solution of the Time-Fractional Hirota-Satsuma Korteweg-de Vries System

In the present work, we consider the nonlinear time-fractional Hirota-Satsuma KdV (Korteweg-de Vries) system in the sense of the Riemann-Liouville fractional calculus and the Erdelyi-Kober fractional calculus. By appealing to Lie group analysis, we derive the symmetry groups of transformations under which the given equations remain invariant. We also construct the symmetry reductions and particular group invariant solutions for the given system of equations. Finally, in order to highlight the importance of the study, the physical significance of the solution, which is described in this paper, is investigated and illustrated graphically.