Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models

Tarasov, V.E.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 4 сентября 2019 г.

Автор: Tarasov Vasily E.
Журнал: Mathematics
Том: 7
Номер: 6
Год издания: 2019
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Первая страница: 554-1
Последняя страница: 554-50
DOI: 10.3390/math7060554
Аннотация: This article is a review of problems and difficulties arising in the construction of fractional-dynamic analogs of standard models by using fractional calculus. These fractional generalizations allow us to take into account the effects of memory and non-locality, distributed lag, and scaling. We formulate rules (principles) for constructing fractional generalizations of standard models, which were described by differential equations of integer order. Important requirements to building fractional generalization of dynamical models (the rules for “fractional-dynamic generalizers”) are represented as the derivability principle, the multiplicity principle, the solvability and correspondence principles, and the interpretability principle. The characteristic properties of fractional derivatives of non-integer order are the violation of standard rules and properties that are fulfilled for derivatives of integer order. These non-standard mathematical properties allow us to describe non-standard processes and phenomena associated with non-locality and memory. However, these non-standard properties lead to restrictions in the sequential and self-consistent construction of fractional generalizations of standard models. In this article, we give examples of problems arising due to the non-standard properties of fractional derivatives in construction of fractional generalizations of standard dynamic models in economics
Добавил в систему: Тарасов Василий Евгеньевич

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Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Modelsстатья

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