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In recent years, because complex networks can be used to model real-world complex systems, such as the Internet, urban infrastructure networks, and gene interaction networks, such research has been widely applied in engineering, social sciences, and life sciences and has caused widespread concern. Fractal dimension, as a concept concerning the filling ability and complexity of an object space, has great significance for the study of the robustness of complex networks. This paper studies the relationship between fractal dimension and the robustness of different types of complex networks from the perspective of network structure and network scale. We find that fractal dimension is strongly correlated with robustness under certain conditions and can be used as an important index to evaluate the robustness of complex networks.

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This paper investigates the Hadamard fractional calculus of a fractal function. It is proved that there exists some linear relationship between the order of Hadamard fractional calculus and the fractal dimension of the Weierstrass function including Box dimension, [Formula: see text]-dimension and Packing dimension. Furthermore, numerical result is given to show the linear relationship.