(untitled) (Contemporary Mathematics, 2025)
The paper discusses the application of the Residual Power Series Conformable Method (RPSCM) and a new iteration method to solve the fractional nonlinear Harry-Dym and Rosenau-Hyman to employ conformable fractional derivatives. The suggested techniques focus on the non-linearity and high dimensionality of these equations and would provide sufficiently accurate and efficient approximate solutions. The RPSCM combines a power series expansion and residual error correction, whereas the iterative method enhances convergence by employing a distinct approach. The graphical and numerical performances of the two methods are compelling, as the figures represent the simulated solution behaviors and the sensitive changes resulting from variations in the fractional order. The superior precision of the techniques is also evident when the results obtained by the methods are compared with standards presented in tables in solving nonlinear fractional problems across various applied fields.