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In this paper, higher order renditions of two popular numerical methods are proposed for the precise modeling of fractal antenna array structures. Particularly, a higher order finite difference time domain (FDTD) method, which introduces nonstandard differential operators, and second-order curl-conforming vector finite elements with optimized convergence behavior are considered. These techniques attain sufficient accuracy and reduced dispersion errors, even when coarse discretizations are utilized and, therefore, are more preferable compared to lower order approaches, especially in the case of large computational domains. Their enhanced performance is exploited for the rigorous investigation of the radiation properties of several fractal arrays with complex geometrical features.