Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel

Zubair Ahmad; Farhad Ali; Naveed Khan; Ilyas Khan

doi:10.1016/j.chaos.2021.111602

Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel

Zubair Ahmad, Farhad Ali, Naveed Khan, Ilyas Khan

Research output: Contribution to journal › Article › peer-review

45 Citations (Scopus)

Abstract

Fractal-fractional operators have been crucial in detecting some hidden chaotic phenomena that could not be exposed using classical or simple fractional differential and integral operators. To provide new possibilities for capturing more chaotic behaviors, the present study is carried out for the dynamics of a new chaotic system by implementing fractal-fractional differential operator of Mittag-Leffler type kernel. It is also theoretically proved that the present model will have at least one solution and it will also have a unique solution. Numerical scheme is implemented through MATLAB software for the graphical solution of the proposed problem. Some results are found and portrayed through different graphs.

Original language	English
Article number	111602
Journal	Chaos, Solitons and Fractals
Volume	153
DOIs	https://doi.org/10.1016/j.chaos.2021.111602
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

Fractal-fractional differential operator
Hidden chaotic attractor
Integrated circuit
Mittag-Leffler kernel
New chaotic system
Numerical solution

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10.1016/j.chaos.2021.111602

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title = "Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel",

abstract = "Fractal-fractional operators have been crucial in detecting some hidden chaotic phenomena that could not be exposed using classical or simple fractional differential and integral operators. To provide new possibilities for capturing more chaotic behaviors, the present study is carried out for the dynamics of a new chaotic system by implementing fractal-fractional differential operator of Mittag-Leffler type kernel. It is also theoretically proved that the present model will have at least one solution and it will also have a unique solution. Numerical scheme is implemented through MATLAB software for the graphical solution of the proposed problem. Some results are found and portrayed through different graphs.",

keywords = "Fractal-fractional differential operator, Hidden chaotic attractor, Integrated circuit, Mittag-Leffler kernel, New chaotic system, Numerical solution",

author = "Zubair Ahmad and Farhad Ali and Naveed Khan and Ilyas Khan",

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T1 - Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel

AU - Ahmad, Zubair

AU - Ali, Farhad

AU - Khan, Naveed

AU - Khan, Ilyas

PY - 2021/12

Y1 - 2021/12

N2 - Fractal-fractional operators have been crucial in detecting some hidden chaotic phenomena that could not be exposed using classical or simple fractional differential and integral operators. To provide new possibilities for capturing more chaotic behaviors, the present study is carried out for the dynamics of a new chaotic system by implementing fractal-fractional differential operator of Mittag-Leffler type kernel. It is also theoretically proved that the present model will have at least one solution and it will also have a unique solution. Numerical scheme is implemented through MATLAB software for the graphical solution of the proposed problem. Some results are found and portrayed through different graphs.

AB - Fractal-fractional operators have been crucial in detecting some hidden chaotic phenomena that could not be exposed using classical or simple fractional differential and integral operators. To provide new possibilities for capturing more chaotic behaviors, the present study is carried out for the dynamics of a new chaotic system by implementing fractal-fractional differential operator of Mittag-Leffler type kernel. It is also theoretically proved that the present model will have at least one solution and it will also have a unique solution. Numerical scheme is implemented through MATLAB software for the graphical solution of the proposed problem. Some results are found and portrayed through different graphs.

KW - Fractal-fractional differential operator

KW - Hidden chaotic attractor

KW - Integrated circuit

KW - Mittag-Leffler kernel

KW - New chaotic system

KW - Numerical solution

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SN - 0960-0779

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JO - Chaos, Solitons and Fractals

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Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel

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