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Control and Stability Assessment of a Fractal-Fractional Order Finance System |
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PP: 87-104 |
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doi:10.18576/pfda/120106
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Author(s) |
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Muhammad Farman,
Abdul Sattar Ghaffari,
David Amilo,
Zubaria Parvez,
Aseel Smerat,
Mohamed Hafez,
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Abstract |
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| A novel differential operator is presented that combines fractional and fractal differentiation with a number of different kernels. The connection between fractional calculus and fractals is well-known in the literature, and fractal economic processes are thought to offer more realistic models for economic and financial market issues than traditional models. In order to create a mathematical model for a chaotic financial system that incorporates price measure, investment demands, and minimum rate of interest characteristics, a novel chaotic finance system with a minimal interest rate is built utilizing an extended Mittag-Leffler kernel. We analyze the suggested model using fundamental equations, fixed point notions, and local and global stability. With an emphasis on fractional-order systems, Chaos Control is utilized to control linear reactions. In order to guarantee stability and influence at equilibrium points, the controlled design makes sure that solutions are limited within the possible domain and have an influence at lower minimum interest rates. Using Newton’s polynomial-based algorithm, several scenarios are conducted to explore the implications of fractional order and fractal dimension. The results, which were compared using various kernels, are shown by the proportion of minimum interest rates in various countries. In tackling financial and economic growth policy, the results of this study are noteworthy and innovative.
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