125773 20241125101134.0 doi 10.3390/math11071630 sideral 133360 ART-2023-133360 eng Martín, Andrés Fractional-modified Bessel Function of the first kind of integer order 2023 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/MCIU/PID2019-107603GB-I00 info:eu-repo/grantAgreement/ES/MICINN/CEX2021-001164-M info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.3 2023 MATHEMATICS 21 / 490 = 0.043 2023 Q1 T1 0.475 2023 Engineering (miscellaneous) 2023 Q2 Mathematics (miscellaneous) 2023 Q2 Computer Science (miscellaneous) 2023 Q2 4.0 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Estrada, Ernesto 11, 7 (2023), 1630 [13 pp.] Mathematics (Basel) Mathematics 2227-7390 422701 http://zaguan.unizar.es/record/125773/files/texto_completo.pdf Versión publicada 1928191 http://zaguan.unizar.es/record/125773/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:125773 articulos driver 2024-11-22-11:59:56 ARTICLE