000125773 001__ 125773 000125773 005__ 20241125101134.0 000125773 0247_ $$2doi$$a10.3390/math11071630 000125773 0248_ $$2sideral$$a133360 000125773 037__ $$aART-2023-133360 000125773 041__ $$aeng 000125773 100__ $$aMartín, Andrés 000125773 245__ $$aFractional-modified Bessel Function of the first kind of integer order 000125773 260__ $$c2023 000125773 5060_ $$aAccess copy available to the general public$$fUnrestricted 000125773 5203_ $$aThe 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. 000125773 536__ $$9info:eu-repo/grantAgreement/ES/MCIU/PID2019-107603GB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/CEX2021-001164-M 000125773 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000125773 590__ $$a2.3$$b2023 000125773 592__ $$a0.475$$b2023 000125773 591__ $$aMATHEMATICS$$b21 / 490 = 0.043$$c2023$$dQ1$$eT1 000125773 593__ $$aEngineering (miscellaneous)$$c2023$$dQ2 000125773 593__ $$aMathematics (miscellaneous)$$c2023$$dQ2 000125773 593__ $$aComputer Science (miscellaneous)$$c2023$$dQ2 000125773 594__ $$a4.0$$b2023 000125773 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000125773 700__ $$aEstrada, Ernesto 000125773 773__ $$g11, 7 (2023), 1630 [13 pp.]$$pMathematics (Basel)$$tMathematics$$x2227-7390 000125773 8564_ $$s422701$$uhttps://zaguan.unizar.es/record/125773/files/texto_completo.pdf$$yVersión publicada 000125773 8564_ $$s1928191$$uhttps://zaguan.unizar.es/record/125773/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000125773 909CO $$ooai:zaguan.unizar.es:125773$$particulos$$pdriver 000125773 951__ $$a2024-11-22-11:59:56 000125773 980__ $$aARTICLE