Entropy Analysis of Soccer Dynamics

Lopes, António M.; Machado, J. A. Tenreiro

doi:10.3390/e21020187

Cited by 24 publications

(18 citation statements)

References 47 publications

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“…The KdV equations of order three and five have been discussed in [ 3 ] by using two numerical methods. Entropies based on fractional calculus [ 7 ], integer and fractional dynamical systems can be solved by entropy analysis [ 8 ], nonlinear partial differential equations [ 9 ] in entropy and convexity, as well as ractional derivative advection–diffusion in two-dimensional semi-conductor systems and the dynamics of a national soccer league [ 10 , 11 ]. The exact solution to differential equations (DEs) of fractional order with mixed partial derivatives [ 12 ] are fractional linear differential equations with constant coefficients in Laplace transform [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Shah

Khan

Arif

et al. 2019

Entropy

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In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

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Section: Introductionmentioning

confidence: 99%

Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Shah

Khan

Arif

et al. 2019

Entropy

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show abstract

“…Entropy, information theory and fractional calculus tools, have been also recently applied for studying the dynamics of a national soccer league. The complex system state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen-Shannon divergence [39].…”

Section: Some Notes On Fractional Calculusmentioning

confidence: 99%

Model Order Reduction: A Comparison between Integer and Non-Integer Order Systems Approaches

Caponetto

Machado

Murgano

et al. 2019

Entropy

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In this paper, classical and non-integer model order reduction methodologies are compared. Non integer order calculus has been used to generalize many classical control strategies. The property of compressing information in modelling systems, distributed in time and space, and the capability of describing long-term memory effects in dynamical systems are two features suggesting also the application of fractional calculus in model order reduction. In the paper, an open loop balanced realization is compared with three approaches based on a non-integer representation of the reduced system. Several case studies are considered and compared. The results confirm the capability of fractional order systems to capture and compress the dynamics of high order systems.

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“…An approximate solution for fractional differentiation of the generalized Mittag Leffler law by means of exponential decay was discussed in [6], and Kilbas et al discussed various applications of FDEs in [7]. Exact solutions to the FDEs and Laplace Transform of FDEs [8,9], have been things such as fractional dynamical systems [10], entropy and convexity PDEs [11], entropy analysis of soccer dynamics [12], the Laplace homotopy analysis method (LHAM) [13], and the new analytical technique (NAT) [14].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

et al. 2019

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In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

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Entropy Analysis of Soccer Dynamics

Cited by 24 publications

References 47 publications

Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Model Order Reduction: A Comparison between Integer and Non-Integer Order Systems Approaches

An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

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