Approximate Conservation Laws and Symmetry Operators for Fractional Differential Harry-Dym Equation with a Small Perturbation Parameter

The approximate Lie group analysis of differential equations is applied in order to find symmetry operators of time-fractional Harry-Dym equation. First the method of finding symmetries is extended to approximate fractional differential equations and the corresponding reduced form of the equation are derived. The Riemann-Liouville and Caputo definitions are used in this case. Then, the perturbed conservation laws are computed with the modified version of Noether’s theorem based on the formal Lagrangian.