Open AccessModelling chaotic dynamical attractor with fractal-fractional differential operators
Author(s) -
Sonal Jain,
Youssef ElKhatib
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021795
Subject(s) - attractor , chaotic , differential (mechanical device) , mathematics , fourier integral operator , microlocal analysis , fractal , fractal dimension , differential operator , dynamical systems theory , pseudo differential operator , dimension (graph theory) , mathematical analysis , operator theory , pure mathematics , computer science , physics , semi elliptic operator , artificial intelligence , hypoelliptic operator , quantum mechanics , thermodynamics
Differential operators based on convolution have been recognized as powerful mathematical operators able to depict and capture chaotic behaviors, especially those that are not able to be depicted using classical differential and integral operators. While these differential operators have being applied with great success in many fields of science, especially in the case of dynamical system, we have to confess that they were not able depict some chaotic behaviors, especially those with additionally similar patterns. To solve this issue new class of differential and integral operators were proposed and applied in few problems. In this paper, we aim to depict chaotic behavior using the newly defined differential and integral operators with fractional order and fractal dimension. Additionally we introduced a new chaotic operators with strange attractors. Several simulations have been conducted and illustrations of the results are provided to show the efficiency of the models.