Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers

Abstract

This paper presents one way to define an uncountable family of fractional fixed-point methods through a set of matrices that can generate a group of fractional matrix operators, as well as one way to define groups of fractional operators that are isomorphic to the group of integers under the addition, and shows one way to classify and accelerate the order of convergence of the family of proposed iterative methods, which may be useful to continue expanding the applications of the fractional operators. The proposed method to accelerate the order of convergence is used in a fractional iterative method, and with the obtained method are solved simultaneously two nonlinear algebraic systems that depend on time-dependent parameters, and that allow obtaining the temperatures and efficiencies of a hybrid solar receiver. Finally, two uncountable families of fractional fixed-point methods are presented, in which the proposed method to accelerate convergence can be implemented.