Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

Naveed Khan, Zubair Ahmad, Jamal Shah, Saqib Murtaza, M. Daher Albalwi, Hijaz Ahmad, Jamel Baili, Shao Wen Yao

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

Original languageEnglish
Article number5043
JournalScientific Reports
Volume13
Issue number1
DOIs
Publication statusPublished - Dec 2023
Externally publishedYes

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