Open AccessNumerical solution of a fractal-fractional order chaotic circuit system
Author(s) -
Muhammad Altaf Khan,
Abdon Atangana,
Taseer Muhammad,
Ebraheem Alzahrani
Publication year - 2021
Publication title -
revista mexicana de física/revista mexicana de física
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.181
H-Index - 25
eISSN - 2683-2224
pISSN - 0035-001X
DOI - 10.31349/revmexfis.67.051401
Subject(s) - fractal , attractor , fractal derivative , chaotic , fractional calculus , ordinary differential equation , work (physics) , mathematics , exponential function , statistical physics , differential equation , fractal dimension , computer science , mathematical analysis , fractal analysis , physics , artificial intelligence , thermodynamics
The dynamical system has an important research area and due to its wide applications many researchers and scientists working to develop new model and techniques for their solution. We present in this work the dynamics of a chaotic model in the presence of newly introduced fractal-fractional operators. The model is formulated initially in ordinary differential equations and then we utilize the fractal-fractional (FF) in power law, exponential and Mittag-Leffler to generalize the model. For each fractal-fractional order model, we briefly study its numerical solution via the numerical algorithm. We present some graphical results with arbitrary order of fractal and fractional orders, and present that these operators provide different chaotic attractors for different fractal and fractional order values. The graphical results demonstrate the effectiveness of the fractal-fractional operators.