CHAOTIC BEHAVIOR OF MODIFIED STRETCH–TWIST–FOLD FLOW UNDER FRACTAL-FRACTIONAL DERIVATIVES

A. Dlamini, Emile F. Doungmo Goufo and M. Khumalo
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A. Dlamini: Department of Mathematical Sciences, University of South Africa, Cnr Christian de Wet Road and Pioneer Avenue, Florida 1709, Roodepoort, South Africa
Emile F. Doungmo Goufo: Department of Mathematical Sciences, University of South Africa, Cnr Christian de Wet Road and Pioneer Avenue, Florida 1709, Roodepoort, South Africa
M. Khumalo: Department of Mathematical Sciences, University of South Africa, Cnr Christian de Wet Road and Pioneer Avenue, Florida 1709, Roodepoort, South Africa

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-30

Abstract: The application of the recently proposed integral and differential operators known as the fractal-fractional derivatives and integrals has opened doors to ongoing research in different fields of science, engineering, and technology. These operators are a convolution of the fractal derivative with the generalized Mittag-Leffler function with Delta-Dirac property, the power law, and the exponential decay law with Delta-Dirac property. In this paper, we aim to extend the work in the literature by applying these operators to a modified stretch–twist–fold (STF) flow based on the STF flow related to the motion of particles in fluids that naturally occur in the dynamo theorem. We want to capture the dynamical behavior of the modified STF flow under these operators. We will present the numerical schemes that can be used to solve these nonlinear systems of differential equations. We will also consider numerical simulations for different values of fractional order and fractal dimension.

Keywords: Fractal-Fractional Derivatives and Integrals; Stretch–Twist–Fold (STF) Flow; Numerical Scheme (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402071

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