Abstract

KHAN, Muhammad Altaf; ATANGANA, A.; MUHAMMAD, Taseer  and  ALZAHRANI, Ebraheem. Numerical solution of a fractal-fractional order chaotic circuit system. Rev. mex. fis. [online]. 2021, vol.67, n.5, 051401.  Epub Mar 28, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.67.051401.

The dynamical system has an important research area and, due to its wide applications, many researchers and scientists are working to develop new models and techniques for their solution. In this work, 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.

Keywords : Fractal-fractional operators; chaotic model; numerical results; 05.45.-a; 05.40.-a; 02.60.Cb.