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

Vasily E. Tarasov
Additional contact information
Vasily E. Tarasov: Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia

Mathematics, 2019, vol. 7, issue 6, 1-50

Abstract: 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.

Keywords: fractional calculus; fractional dynamics; fractional generalization; long memory; non-locality; mathematical economics; economic theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/6/554/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/6/554/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:6:p:554-:d:240669

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().