A fractional rate model of learning

Dassios, George; Fragoyiannis, George; Satrazemi, Konstantia

doi:10.7153/fdc-06-19

Cited by 3 publications

(3 citation statements)

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“…Specifically, the generalization of the economic model of natural growth with power-law memory suggested in [10] applied the fractional differential equation to investigate the proportional relationship between the income and the growth rate of the output. [45] presented a method to estimate the rate at which the human brain learns a certain amount of knowledge is proportional to the amount of knowledge yet to be learned by using the fractional differential equation.…”

Section: )mentioning

confidence: 99%

“…Note that the fractional calculus has been widely adopted to depict the memory effect in multiple disciplines such as economics, e.g., [10], [29], and human science, e.g., [45], [46]. Specifically, the generalization of the economic model of natural growth with power-law memory suggested in [10] applied the fractional differential equation to investigate the proportional relationship between the income and the growth rate of the output.…”

Section: B the Concept Of The Power-law Memorymentioning

confidence: 99%

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Dynamic Model for Network Selection in Next Generation HetNets With Memory-Affecting Rational Users

Feng

Niyato

et al. 2021

IEEE Trans. on Mobile Comput.

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Recently, due to the staggering growth of wireless data traffic, heterogeneous networks have drawn tremendous attention due to the capabilities of enhancing the capacity/coverage and to save energy consumption for the next generation wireless networks. In this paper, we study a long-run user-centric network selection problem in the 5G heterogeneous network, where the network selection strategies of the users can be investigated dynamically. Unlike the conventional studies on the long-run model, we incorporate the memory effect and consider the fact that the decision-making of the users is affected by their memory, i.e., their past service experience. Namely, the users select the network based on not only their instantaneous achievable service experience but also their past service experience within their memory. Specifically, we model and study the interaction among the users in the framework of fractional evolutionary game based on the classical evolutionary game theory and the concept of the power-law memory. We analytically prove that the equilibrium of the fractional evolutionary game exists, is unique and uniformly stable. We also numerically demonstrate the stability of the fractional evolutionary equilibrium. Extensive numerical results have been conducted to evaluate the performance of the fractional evolutionary game. The numerical results have revealed some insightful findings. For example, the user in the fractional evolutionary game with positive memory effect can achieve a higher cumulative utility compared with the user in the fractional evolutionary game with negative memory effect. Moreover, the fractional evolutionary game with positive memory effect can reduce the loss in the user's cumulative utility caused by the small-scale fading. 2 Network selection, fractional evolutionary game, memory-affecting rationality, and heterogeneous network.

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Section: )mentioning

confidence: 99%

Section: B the Concept Of The Power-law Memorymentioning

confidence: 99%

Dynamic Model for Network Selection in Next Generation HetNets With Memory-Affecting Rational Users

Feng

Niyato

et al. 2021

IEEE Trans. on Mobile Comput.

View full text Add to dashboard Cite

show abstract

“…In the last thirty years, research concerning applications of fractionalorder dynamics has made profound and significant progress. Examples include the time-fractional damage model for hyperelastic body (e.g., to mimic the abdominal aortic aneurysm phenomena [12]), fractional-order models of long memory processes (e.g., the steelmaking process [13]), the fractional-order model of learning [14], fractional-order models in viscoelasticity [15], and economics [16,17]. In particular, fractional calculus was also introduced into the modeling of multi-agent systems.…”

Section: Introductionmentioning

confidence: 99%