Open AccessOn three dimensional fractal dynamics with fractional inputs and applications
Author(s) -
Emile Franc Doungmo Goufo,
Abdon Atangana
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022114
Subject(s) - fractal , fractional calculus , operator (biology) , mathematics , fractal derivative , order (exchange) , exponential function , mathematical analysis , fractal analysis , fractal dimension , biochemistry , chemistry , repressor , transcription factor , gene , finance , economics
The environment around us naturally represents number of its components in fractal structures. Some fractal patterns are also artificially simulated using real life mathematical systems. In this paper, we use the fractal operator combined to the fractional operator with both exponential and Mittag-leffler laws to analyze and solve generalized three-dimensional systems related to real life phenomena. Numerical solutions are provided in each case and applications to some related systems are given. Numerical simulations show the existence of the models' initial three-dimensional structure followed by its self- replication in fractal structure mathematically produced. The whole dynamics are also impacted by the fractional part of the operator as the derivative order changes.