Sets of fractional operators and numerical estimation of the order of convergence of a family of fractional fixed point methods

10/01/2021
by   A. Torres-Hernandez, et al.
0

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simplified and compact way to work the fractional calculus through the classification of fractional operators using sets. This new way of working with fractional operators, which may be called as fractional calculus of sets, allows to generalize objects of the conventional calculus such as tensor operators, the diffusion equation, the heat equation, the Taylor series of a vector-valued function, and the fixed point method in several variables which allows to generate the method known as the fractional fixed point method. It is also shown that each fractional fixed point method that generates a convergent sequence has the ability to generate an uncountable family of fractional fixed point methods that generate convergent sequences. So, it is shown one way to estimate numerically the mean order of convergence of any fractional fixed point method in a region Ω through the problem of determining the critical points of a scalar function, and it is shown how to construct a hybrid fractional iterative method to determine the critical points of a scalar function.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/10/2023

Finite dimensional approximation to fractional stochastic integro-differential equations with non-instantaneous impulses

This manuscript proposes a class of fractional stochastic integro-differ...
research
01/29/2020

About Convergence and Order of Convergence of some Fractional Derivatives

In this paper we establish some convergence results for Riemann-Liouvill...
research
04/19/2021

BDF6 SAV schemes for time-fractional Allen-Cahn dissipative systems

Recently, the error analysis of BDFk (1⩽ k⩽5) SAV (scalar auxiliary vari...
research
06/25/2020

An approximation to zeros of the Riemann zeta function using fractional calculus

A novel iterative method to approximate the zeros of the Riemann zeta fu...
research
04/24/2021

On system rollback and totalised fields

In system operations it is commonly assumed that arbitrary changes to a ...
research
04/27/2021

Queues with Updating Information: Finding the Amplitude of Oscillations

Many service systems provide customers with information about the system...

Please sign up or login with your details

Forgot password? Click here to reset