ArticleScientific reports2023
Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel.
Article in Scientific reports, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- A numerical framework for fractional and fractal-fractional analysis of the Pehlivan chaotic system using Caputo derivative.Scientific reports · 2026Article
- Impact of nanoparticles on vegetable oil as a cutting fluid with fractional ramped analysis.Scientific reports · 2023Article
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Authors and funding
8 authors.
Funding
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.
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