Formulation of Conformable Time Fractional Differential Equation and q-HAM Solution Comparison with ADM

In this paper, the semi-inverse method is used to obtain the Lagrangian of the regular Harry Dym (HD) equation. The classical derivatives in the obtained Lagrangian are replaced by the fractional derivatives. The fractional Euler-Lagrange equation leads to the fractional HD equation. The conformable fractional derivative is used to obtain the time fractional HD equation. The Adomians decomposition method (ADM) and q-Homotopy analysis method (q-HAM) are employed to solve the formulated fractional equation. Comparisons are made with ADM, q-HAM and the exact solutions for alpha = 1. Numerical results are demonstrated by tables and graphs for alpha = 1 and 0.9.