Affiliation:
1. STAR-UBB Institute, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Abstract
This paper deepens some results on a Mandelbrot set and Julia sets of Caputo’s fractional order. It is shown analytically and computationally that the classical Mandelbrot set of integer order is a particular case of Julia sets of Caputo-like fractional order. Additionally, the differences between the fractional-order Mandelbrot set and Julia sets from their integer-order variants are revealed. Equipotential lines and external rays of a Mandelbrot set and Julia sets of fractional order are determined.
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