Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations

Agarwal, Ravi P.; Hristova, Snezhana; O’Regan, Donal

doi:10.3390/sym13040730

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…Then, it will be possible to stabilize the profitability of revenues in time by a targeted reduction in the variability of this quantity, i.e., by minimizing sd 1 − AVC×q TR . This view is sometimes, in the literature or in published research (e.g., [24,25]), referred to as statistical stability regulation. For the stability of mass processes, it was derived and used, for example, in a ( [15]) mass process based on the Six Sigma concept.…”

Section: Resultsmentioning

confidence: 99%

“…There are different distributions of the random variable different from the normal ones covering the uncertainty of production and distribution. The stability of financial variables is considered to be the main attribute of sustainability of a given business in invariant environmental conditions [24,25]. Statistical regulation requires a sufficient number of data and the normality of the data distribution, and the independence of the data (without the existence of autocorrelation) also requires a constant variance and mean value, monitoring of only one character (quantity) within financial management on a single product [26].…”

Section: Methodsmentioning

confidence: 99%

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Financial Stability Control for Business Sustainability: A Case Study from Food Production

Macak¹

2022

Mathematics

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Conventional financial management methods, based on extrapolation approaches to financial analysis, often reach their limits due to violations of stationary controlled financial variables, for example, interventions in the economy and social life necessary to manage the COVID-19 pandemic. Therefore, we have created a procedure for controlling financial quantities, which respects the non-stationarity of the controlled quantity using the maximum control deviation covering the confidence interval of a random variable or random vector. For this interval, we then determined the algebraic criteria of the transfer functions using the Laplace transform. For the Laplace transform, we determined the theorem on the values of the stable roots of the characteristic equation, including the deductive proof. This theorem is directly usable for determining the stability of the management for selected financial variables. For the practical application, we used the consistency of the stable roots of the characteristic equation with the Stodola and Hurwitz stability conditions. We demonstrated the procedure for selected quantities of financial management in food production. In conclusion, we proposed a control mechanism for the convergence of regulatory deviation using a combination of proportional and integration schemes. We also determined the diversification of action interventions (into development, production, and marketing) using a factorial design.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Financial Stability Control for Business Sustainability: A Case Study from Food Production

Macak¹

2022

Mathematics

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“…The paper [15] is devoted to the mathematical analysis of a fractional differential equation. Specifically, the paper deals with a system of nonlinear Riemann-Liouville fractional differential equations with non-instantaneous impulses.…”

Section: Introductionmentioning

confidence: 99%

Special Issue: Symmetry in Nonequilibrium Statistical Mechanics and Dynamical Systems

Bianca

2022

Symmetry

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The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerging phenomena occurring in nature and society. This editorial article introduces the topic and the contributions of this Special Issue. This Special Issue focuses, on the one hand, on the development of new methods, frameworks and models coming from dynamical system theory and the equilibrium/non-equilibrium statistical mechanics and, on the other hand, opens problems related to the existing frameworks. The Special Issue also includes applications to physical, biological and engineering systems.

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“…Fractional calculus and fractal calculus have attracted much attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] due to the increasing number of applications in different fields. Among them, the two-scale fractal theory developed by He et al [17][18][19] is effectively established for dealing with many discontinuous problems; the local fractional derivative (LFD) [5,20,21] can be adopted to solve some non-differentiable problems.…”

Section: Introductionmentioning

confidence: 99%

Riemann–Hilbert Approach for Constructing Analytical Solutions and Conservation Laws of a Local Time-Fractional Nonlinear Schrödinger Type Equation

Zhang

2021

Symmetry

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Fractal and fractional calculus have important theoretical and practical value. In this paper, analytical solutions, including the N-fractal-soliton solution with fractal characteristics in time and soliton characteristics in space as well as the long-time asymptotic solution of a local time-fractional nonlinear Schrödinger (NLS)-type equation, are obtained by extending the Riemann–Hilbert (RH) approach together with the symmetries of the associated spectral function, jump matrix, and solution of the related RH problem. In addition, infinitely many conservation laws determined by an expression, one end of which is the partial derivative of local fractional-order in time, and the other end is the partial derivative of integral order in space of the local time-fractional NLS-type equation are also obtained. Constraining the time variable to the Cantor set, the obtained one-fractal-soliton solution is simulated, which shows the solution possesses continuous and non-differentiable characteristics in the time direction but keeps the soliton continuous and differentiable in the space direction. The essence of the fractal-soliton feature is that the time and space variables are set into two different dimensions of 0.631 and 1, respectively. This is also a concrete example of the same object showing different geometric characteristics on two scales.

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Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations

Cited by 4 publications

References 17 publications

Financial Stability Control for Business Sustainability: A Case Study from Food Production

Financial Stability Control for Business Sustainability: A Case Study from Food Production

Special Issue: Symmetry in Nonequilibrium Statistical Mechanics and Dynamical Systems

Riemann–Hilbert Approach for Constructing Analytical Solutions and Conservation Laws of a Local Time-Fractional Nonlinear Schrödinger Type Equation

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