Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets

Abstract In this paper, we present a semi-analytic method called the local fractional homotopy analysis method (LFHAM) for solving differential equations involving local fractional derivatives based on the local fractional calculus and the homotopy analysis method. The suggested analytical technique always provides a simple way of constructing a series of solutions from the higher-order deformation equation. The LFHAM guarantees the convergence of the series solutions using the nonzero convergence-control parameter. Three examples are provided to illustrate the efficiency and high accuracy of the method