Advantages of a limited frequency band fractional integration operator in the definition of fractional models

2019 ◽  
Author(s):  
Jocelyn Sabatier ◽  
Sergio Rodriguez Cadavid ◽  
Christophe Farges
Keyword(s):  
Frequency Band ◽  
Fractional Integration ◽  
Integration Operator ◽  
Fractional Integration Operator ◽  
Fractional Models ◽  
Limited Frequency ◽  
Definition Of

scholarly journals A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Stefan Samko
Keyword(s):  
Fractional Integration ◽  
Fractional Integrals ◽  
Variable Order ◽  
Integration Operator ◽  
Hölder Continuous ◽  
Open Set ◽  
Fractional Integration Operator ◽  
Limiting Case

AbstractWe show that the Riesz fractional integration operator I α(·) of variable order on a bounded open set in Ω ⊂ ℝn in the limiting Sobolev case is bounded from L p(·)(Ω) into BMO(Ω), if p(x) satisfies the standard logcondition and α(x) is Hölder continuous of an arbitrarily small order.

scholarly journals Fractional integration operator of variable order in the holder spacesHλ(x)

1995 ◽  
Vol 18 (4) ◽  
pp. 777-788 ◽  
Author(s):  
Bertram Ross ◽  
Stefan Samko
Keyword(s):  
Fractional Integration ◽  
Fractional Integrals ◽  
Variable Order ◽  
Integration Operator ◽  
Fractional Integration Operator ◽  
Type Spaces ◽  
Littlewood Theorem

The fractional integralsIa+α(x)φof variable orderα(x)are considered. A theorem on mapping properties ofIa+α(x)φin Holder-type spacesHλ(x)is proved, this being a generalization of the well known Hardy-Littlewood theorem.

Weighted adams type theorem for the riesz fractional integral in generalized morrey space

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Evgeniya Burtseva ◽  
Natasha Samko
Keyword(s):  
Fractional Integral ◽  
Morrey Space ◽  
Fractional Integration ◽  
Type Theorem ◽  
Integration Operator ◽  
Generalized Morrey Space ◽  
Fractional Integration Operator

AbstractWe prove the boundedness of the Riesz fractional integration operator from a generalized Morrey space

scholarly journals Fractional State Space Description: A Particular Case of the Volterra Equations

2020 ◽  
Vol 4 (2) ◽  
pp. 23 ◽  
Author(s):  
Jocelyn Sabatier
Keyword(s):  
State Space ◽  
Power Law ◽  
Fractional Integration ◽  
Volterra Equations ◽  
Time Range ◽  
Fast Time ◽  
Memory Length ◽  
Fractional Models ◽  
Definition Of ◽  
Space Description

To tackle several limitations recently highlighted in the field of fractional differentiation and fractional models, some authors have proposed new kernels for the definition of fractional integration/differentiation operators. Some limitations still remain, however, with these kernels, whereas solutions prior to the introduction of fractional models exist in the literature. This paper shows that the fractional pseudo state space description, a fractional model widely used in the literature, is a special case of the Volterra equations, equations introduced nearly a century ago. Volterra equations can thus be viewed as a serious alternative to fractional pseudo state space descriptions for modelling power law type long memory behaviours. This paper thus presents a new class of model involving a Volterra equation and several kernels associated with this equation capable of generating power law behaviours of various kinds. One is particularly interesting as it permits a power law behaviour in a given frequency band and, thus, a limited memory effect on a given time range (as the memory length is finite, the description does not exhibit infinitely slow and infinitely fast time constants as for pseudo state space descriptions).

Numerical Simulations of Fractional Systems

2003 ◽  
Author(s):  
Mohamed Aoun ◽  
Rachid Malti ◽  
Franc¸ois Levron ◽  
Alain Oustaloup
Keyword(s):  
Numerical Simulations ◽  
Continuous Time ◽  
Fractional Integration ◽  
Integration Operator ◽  
Fractional Differentiation ◽  
Fractional Systems ◽  
New Methods ◽  
Fractional Integration Operator ◽  
Poles And Zeros ◽  
Continuous Time Models

This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation.

Fractional integration operator on some radial rays and intertwining for the Dunkl operator

2016 ◽  
Vol 19 (3) ◽  
Author(s):  
Fethi Bouzeffour
Keyword(s):  
Fractional Calculus ◽  
Cyclic Group ◽  
Fractional Integration ◽  
Integration Operator ◽  
Dunkl Operator ◽  
Reflection Operator ◽  
Bessel Operators ◽  
Finite Cyclic Group ◽  
Generalized Fractional Calculus ◽  
Fractional Integration Operator

AbstractIn this paper we consider the differential-difference reflection operator associated with a finite cyclic group,It is to emphasize that both hyper–Bessel operators and the so-called Poisson–Dimovski transformation (transmutation) are typical examples of the operators of generalized fractional calculus [

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