Fractional models for analysis of economic risks

Rogosin, Sergei; Karpiyenya, Maria

doi:10.1007/s13540-023-00202-y

Cited by 5 publications

(2 citation statements)

References 47 publications

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“…Assume that s * = ϖi = |ϖ|(cos( π 2 ) + i sin(± π 2 )) is one of the pure imaginary roots of Equation (15), where ϖ is a positive real number. Taking s * into Equation ( 15) yields |ϖ| 2q (cos qπ + i sin(±qπ)) − c 22 |ϖ| q (cos qπ 2 + i sin(± qπ 2 ))(cos ϖτ − i sin ϖτ) − a|ϖ| q (cos qπ 2 + i sin(± qπ 2 )) + b(cos ϖτ − i sin ϖτ) + pb 22 = 0.…”

Section: Resultsmentioning

confidence: 99%

“…The study of the complex dynamics of economic systems has become a prominent issue in economics and macroeconomics in recent years. Several nonlinear continuous models have been proposed to explicate the core features of economic data based on the dynamic behavior of the system [6][7][8][9][10][11][12][13][14][15]. The results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior are presented [8].…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of a Fractional-Order Time-Delayed Solow Growth Model with Environmental Pollution

Gu,

Wang

2024

Fractal Fract

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Economic growth is resulting in serious environmental problems. Effectively establishing an economic growth model that considers environmental pollution is an important topic. To analyze the interplay between economic growth and environmental pollution, a fractional-order time-delayed economic growth model with environmental purification is proposed in this paper. The established model considers not only the environment and economic production but also the labor force population and total factor productivity. Furthermore, the asymptotic stability conditions and parameter stability interval are provided. Finally, in numerical experiments, the correctness of the theory is verified.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability Analysis of a Fractional-Order Time-Delayed Solow Growth Model with Environmental Pollution

Gu,

Wang

2024

Fractal Fract

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On the variable-order fractional derivatives with respect to another function

Almeida

2024

Aequat. Math.

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In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and the integral kernel depends on a function. We observe that in the case of variable order, the concepts are distinct, and we present relations between them. Formulas for approximating fractional derivatives are provided, involving only integer-order derivatives. Finally, we conclude the work with some simulations to exemplify the method.

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