| Sammanfattning: | Some existing chaotic systems cannot display dynamics with attractors showing a fractal representation. This is due, not only to the nature of the phenomenon under description, but also to the type of derivative operator used to express the whole model. Now, the question to be asked now is can we use a derivative operator that triggers the appearance of a fractal structure in the dynamics of the system! In this work, we use the fractal-fractional derivative with a fractional order to analyze a multi-dimensional autonomous system that happens to be chaotic with multi-wing attractors. The fractal-fractional operator, which is a combination of fractal process and fractional differentiation, is a relatively new concept whose properties and features are still under investigation. After recalling the basic concepts behind fractal-fractional operator, we analyze the model both in the integer standard case and the generalized case. The integer case reveals that, under certain conditions on the parameters involved, the model is characterized by a two-wing attractor instead of four wings. Due to the impact of such a fractal-fractional operator, the system is able to maintain the two-wing attractor. Additionally, such attractor that can self-replicate in a fractal process and the observe self replication can multiply as the fractal-fractional derivative order changes. This results reveal a great feature of the fractal-fractional derivative with a fractional order, that was still unknown.
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