On three dimensional fractal dynamics with fractional inputs and applications

Emile Franc Doungmo Goufo; Abdon Atangana; Emile Franc Doungmo Goufo; Abdon Atangana

doi:10.3934/math.2022114

AIMS Mathematics

2022, Volume 7, Issue 2: 1982-2000. doi: 10.3934/math.2022114

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On three dimensional fractal dynamics with fractional inputs and applications

Emile Franc Doungmo Goufo ^{1
,
,},
Abdon Atangana ²

1.
Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa
2.
Institute for Groundwater Studies, University of the Free State, Bloemfontein 9300, South Africa

Received: 19 August 2021 Accepted: 24 October 2021 Published: 05 November 2021
MSC : 65P20, 65P30, 28A80, 65J15, 26A33

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.
- three-dimensional fractal patterns,
- fractal-fractional modeling,
- numerical solution,
- exponential and Mittag-leffler laws
Citation: Emile Franc Doungmo Goufo, Abdon Atangana. On three dimensional fractal dynamics with fractional inputs and applications[J]. AIMS Mathematics, 2022, 7(2): 1982-2000. doi: 10.3934/math.2022114

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Abstract

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.

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