Fractional-modified Bessel Function of the first kind of integer order

Martín, Andrés ; Estrada, Ernesto

Resumen: 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.

Idioma: Inglés

DOI: 10.3390/math11071630

Año: 2023

Publicado en: Mathematics 11, 7 (2023), 1630 [13 pp.]
ISSN: 2227-7390

Factor impacto JCR: 2.3 (2023)

Categ. JCR: MATHEMATICS rank: 21 / 490 = 0.043 (2023) - Q1 - T1

Factor impacto CITESCORE: 4.0 - Mathematics (all) (Q1) - Engineering (miscellaneous) (Q2) - Computer Science (miscellaneous) (Q2)

Factor impacto SCIMAGO: 0.475 - Engineering (miscellaneous) (Q2) - Mathematics (miscellaneous) (Q2) - Computer Science (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2019-107603GB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/CEX2021-001164-M

Tipo y forma: Article (Published version)