Solving the Lane-Emden and Emden-Fowler equations on Cantor Sets by the Local Fractional Homotopy Analysis Method

Within the definition of the local fractional derivative, we present a reliable and effective method for solving the Lane- Emden and Emden-Fowler models in the current article. Numerous fields of research and engineering can benefit from the use of these models. The proposed technique is named the local fractional homotopy analysis method. The method is applied for both models of k order and tested for several examples. This method proves to be effective in handling such models when compared to other similar models. The results indicate the robustness of the technique and the possibility of its application to other models in the future.