Sets of fractional operators and some of their applications

Torres Hernandez, Anthony; Brambila Paz, Fernando; Ramírez, Rafael, 1966-

doi:http://dx.doi.org/10.5772/intechopen.107263

Sets of fractional operators and some of their applications

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Citation

Torres-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.107263

Abstract

This 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.