Torres Hernandez, AnthonyBrambila Paz, FernandoRamírez, Rafael, 1966-2024-04-092024-04-092023Torres-Hernandez A, Brambila-Paz F, Ramirez-Melendez R. Sets of fractional operators and some of their applications. In: Abou Jaoudé A, editor. Operator theory - recent advances, new perspectives and applications. London: IntechOpen; 2023. p. 79-96. DOI: 10.5772/intechopen.1072639781838811112http://hdl.handle.net/10230/59707This chapter presents one way to define Abelian groups of fractional operators isomorphic to the group of integers under addition through a family of sets of fractional operators and a modified Hadamard product, as well as one way to define finite Abelian groups of fractional operators through sets of positive residual classes less than a prime number. Furthermore, it is presented one way to define sets of fractional operators which allow generalizing the Taylor series expansion of a vector-valued function in multi-index notation, as well as one way to define a family of fractional fixed-point methods and determine their order of convergence analytically through sets.application/pdfeng©2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in anymedium, provided the originalwork is properly cited.info:eu-repo/semantics/bookParthttp://dx.doi.org/10.5772/intechopen.107263fractional operatorsset theorygroup theoryfractional iterative methodsfractional calculus of setsinfo:eu-repo/semantics/openAccess