A Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients

Francesco Mainardi
Additional contact information
Francesco Mainardi: Department of Physics and Astronomy, University of Bologna, and the National Institute of Nuclear Physics (INFN), Via Irnerio, 46, I-40126 Bologna, Italy

Mathematics, 2018, vol. 6, issue 1, 1-5

Abstract: In this note, we show how an initial value problem for a relaxation process governed by a differential equation of a non-integer order with a constant coefficient may be equivalent to that of a differential equation of the first order with a varying coefficient. This equivalence is shown for the simple fractional relaxation equation that points out the relevance of the Mittag–Leffler function in fractional calculus. This simple argument may lead to the equivalence of more general processes governed by evolution equations of fractional order with constant coefficients to processes governed by differential equations of integer order but with varying coefficients. Our main motivation is to solicit the researchers to extend this approach to other areas of applied science in order to have a deeper knowledge of certain phenomena, both deterministic and stochastic ones, investigated nowadays with the techniques of the fractional calculus.

Keywords: Caputo fractional derivatives; Mittag–Leffler functions; anomalous relaxation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/6/1/8/pdf (application/pdf)
https://www.mdpi.com/2227-7390/6/1/8/ (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:6:y:2018:i:1:p:8-:d:126113

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 ().