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Fractional econophysics: Market price dynamics with memory effects

机译：分数生态物理学：市场价格动态与记忆效应

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In recent years, a new branch of the econophysics has appeared and began to actively develop, which can be called fractional econophysics. We can define fractional econophysics as a new direction of research applying methods developed in physical sciences, to describe processes in economics and finance, basically those including power-law memory and spatial nonlocality. The mathematical tool of this branch of econophysics is the fractional calculus. The birth of the fractional econophysics can be dated 2000 and it can be primarily associated with the works of a group, which includes E. Scalas, F. Mainardi, R. Gorenflo, M. Raberto, in the field of the continuoustime finance. The fractional econophysics was born on the border of the centuries: the first paper was submitted to Physica A on 10 December 1999. Then a lot of work was done on the adaptation and application of fractional dynamics methods, physical model and equations, previously used in the physical sciences, to the description of processes in economics and finance. In fact, at the end of 2019 and at the beginning of 2020 there will be a twenty-year anniversary of fractional econophysics. In this paper, using the fractional econophysics approach, we consider dynamics of market prices, in which power-law memory effects are taken into account. We propose new economic model of the price dynamics in the market for a single product. In this model we assume that economic entities (merchants, buyers, suppliers) can remember how stocks of goods and their prices have changed over time. (C) 2020 Elsevier B.V. All rights reserved.
机译：近年来，出现了一个新的生态物理学分支，并开始积极发展，这可以称为分数生态物理学。我们可以将分数的生态物理学定义为物理科学中开发的研究方法的新方向，以描述经济学和金融的过程，基本上包括幂律记忆和空间非侦察。这种生态物理学分支的数学工具是分数微积分。分数生态物理学的诞生可以进行2000年，它主要与一组的作品相关，其中包括普瑞斯金融领域的E. Scalas，F.Mirmardi，R.Gorenflo，M.Raberto。分数生态物理学出生在几个世纪以来的边界：第一篇论文于1999年12月10日提交给Physica a。然后在分数动力学方法，物理模型和方程式的适应和应用方面完成了大量工作物理科学，经济学和金融过程的描述。事实上，在2019年底和2020年初，将有一个分数仙人掌成立二十周年。在本文中，使用分数的生态物理学方法，我们考虑市场价格的动态，其中考虑了幂律记忆效应。我们为单一产品提出了市场价格动态的新经济模式。在这种模式中，我们假设经济实体（商家，买家，供应商）可以记住货物股票及其价格随着时间的推移而变化。 （c）2020 Elsevier B.v.保留所有权利。

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