Some Fractional Integral and Derivative Formulas Revisited

Juan Luis González-Santander () and Francesco Mainardi
Additional contact information
Juan Luis González-Santander: Department de Mathematics, University of Oviedo, C Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain
Francesco Mainardi: Department of Physics and Astronomy, University of Bologna, and INFN, Via Irnerio 46, I-40126 Bologna, Italy

Mathematics, 2024, vol. 12, issue 17, 1-13

Abstract: In the most common literature about fractional calculus, we find that D t α a f t = I t − α a f t is assumed implicitly in the tables of fractional integrals and derivatives. However, this is not straightforward from the definitions of I t α a f t and D t α a f t . In this sense, we prove that D t 0 f t = I t − α 0 f t is true for f t = t ν − 1 log t , and f t = e λ t , despite the fact that these derivations are highly non-trivial. Moreover, the corresponding formulas for D t α − ∞ t − δ and I t α − ∞ t − δ found in the literature are incorrect; thus, we derive the correct ones, proving in turn that D t α − ∞ t − δ = I t − α − ∞ t − δ holds true.

Keywords: Riemann–Liouville fractional integral; Riemann–Liouville fractional derivative; Weyl fractional integral; Weyl fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/17/2786/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/17/2786/ (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:12:y:2024:i:17:p:2786-:d:1474246

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 ().