Fractional-Modified Bessel Function of the First Kind of Integer Order
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/351638 |
| Acceso en línea: | http://hdl.handle.net/10261/351638 https://api.elsevier.com/content/abstract/scopus_id/85152786375 |
| Access Level: | acceso abierto |
| Palabra clave: | Riemann–Liouville integral Caputo derivative Communicability in graphs Cycles Estrada index Fractional calculus Mittag–Leffler function Modified Bessel functions Paths Power-series |
| Sumario: | 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. |
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