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Hyperchaos remains one of the most complex behaviors in the bifurcation mechanisms and so far, only few hyperchaotic dynamics have been identified experimentally. The construction and design of complex models able to generate hyperchaotic attractors with wings on many rows and columns have become a source of interest for many fractal & chaos theorists, applied physicists and engineers. In this paper, we make use of a simple method, that consists on combining the fractal and fractional operator with L¨u system, in order to generate second class hyperchaotic attractors with wings on many rows and columns. Such a combination yields a modified initial value problem, that is solved both analytically and numerically. We then implement the proposed scheme to perform some graphical representations showing the second class types of attractors in the form n × m-wings, (n, m ∈ N), which appear to be hyperchaotic and exhibit a mirror symmetrical structure. The graphical simulations also depict a process where the lower and upper parts of the second class hyperchaotic attractors are seen to be moving away from the mirror symmetrical junction due to the parameter’s impact of the fractal-fractional operator. [ABSTRACT FROM AUTHOR]

Not every chaotic system has the particularity of displaying attractors with a fractal structure. That is why strange attractors remain enthralling not only for their fractal structure, but also for their amazing chaotic and multi-scroll dynamics. In this work, we apply the non-local and non-singular kernel operator to a four-dimensional chaotic system with two equilibrium points and show the existence of various types of attractors, including the butterfly type and strange type. Recently, there have been virulent communications related to the validity or not of the index law in fractional differentiation with non-local operators. These discussions resulted in pointing out many important features of the Mittag-Leffler function used as kernel and suitable to describe more complex real world problems. This paper follows the same momentum by pointing out another important feature of the non-local and non-singular kernel operator applied to chaotic models. We solve the model numerically and discuss the bifurcation and period doubling dynamics that eventually lead to chaos (in the form of butterfly attractor). Lastly, we provide related numerical simulations which prove the existence of a chaotic fractal structure (strange attractors).