Lie symmetries, exact solutions and conservation laws of time fractional Hunter–Saxton system with variable coefficient

Purpose We aimed to apply Lie symmetry and conservation laws to study time fractional Hunter–Saxton system with variable coefficient, which contains the mixed derivative of the Riemann–Liouville time-fractional derivative and the second order x-derivative. Design/methodology/approach This paper uses Lie symmetry analysis method, power series method, symmetry and conservation. Findings We obtained the convergent power series solutions and conservation laws corresponding to each symmetry. Originality/value Lie symmetry analysis method is applied to a class of nonlinear fractional order partial differential equations, which contains the mixed derivative of the Riemann–Liouville time-fractional derivative and the second order x-derivative. Fractional prolongation formula and fractional Noether operators are derived.