Article
Version 1
Preserved in Portico This version is not peer-reviewed
Fractional Modified Bessel Function of the First Kind of Integer Order
Version 1
: Received: 15 February 2023 / Approved: 27 February 2023 / Online: 27 February 2023 (09:39:57 CET)
A peer-reviewed article of this Preprint also exists.
Martín, A.; Estrada, E. Fractional-Modified Bessel Function of the First Kind of Integer Order. Mathematics 2023, 11, 1630. Martín, A.; Estrada, E. Fractional-Modified Bessel Function of the First Kind of Integer Order. Mathematics 2023, 11, 1630.
Abstract
Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.
Keywords
Modified Bessel functions; Communicability in graphs; Estrada index; Power-series; Fractional calculus; Caputo derivative; Riemann-Liouville integral; Paths; Cycles
Subject
Computer Science and Mathematics, Analysis
Copyright: 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.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
