Next Article in Journal / Special Issue
Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks
Previous Article in Journal / Special Issue
Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives
Article Menu

Export Article

Open AccessArticle
Mathematics 2018, 6(1), 4; doi:10.3390/math6010004

A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability

1
Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy
2
Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
*
Author to whom correspondence should be addressed.
Received: 18 November 2017 / Revised: 24 December 2017 / Accepted: 26 December 2017 / Published: 1 January 2018
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
View Full-Text   |   Download PDF [730 KB, uploaded 1 January 2018]

Abstract

In this paper, we show several connections between special functions arising from generalized Conway-Maxwell-Poisson (COM-Poisson) type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results are obtained, showing the particular role of Hadamard-type derivatives in connection with a recently introduced generalization of the Le Roy function. We are also able to prove a general connection between fractional hyper-Bessel-type equations involving Hadamard operators and Le Roy functions. View Full-Text
Keywords: Hadamard fractional derivatives; COM-Poisson distributions; Modified Mittag–Leffler functions Hadamard fractional derivatives; COM-Poisson distributions; Modified Mittag–Leffler functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Garra, R.; Orsingher, E.; Polito, F. A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability. Mathematics 2018, 6, 4.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top