Abstract
This paper proposes fractional quantum Julia sets based on a fractional q-difference map and preliminarily investigates their fractal dynamic characteristics by numerical methods and graphical explorations. The influence of parameters on the novel fractal sets is performed by dimension analysis. Memory and scale mainly affect the appearance and existence of the sets, respectively. The robustness of the sets to three types of dynamic noise perturbations is discussed by the Julia deviation tools. In particular, the deviation index is fitted concerning noise intensity. Several extensive numerical experiments are done to support the main conclusions.
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