Perturbations of a fractional integration operator

1979 ◽  
Vol 13 (2) ◽  
pp. 145-146 ◽  
Author(s):  
M. M. Malamud
Keyword(s):  
Fractional Integration ◽  
Integration Operator ◽  
Fractional Integration Operator

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

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 [

CONTINUOUS-TIME FRACTIONAL ORDER LINEAR SYSTEMS IDENTIFICATION USING CHEBYSHEV WAVELET

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 23-28
Author(s):  
Shuen Wang ◽  
Ying Wang ◽  
Yinggan Tang
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Integration ◽  
Operational Matrices ◽  
Computation Complexity ◽  
Order Linear ◽  
Fractional Integration Operator ◽  
Systems Identification ◽  
Chebyshev Wavelet

In this paper, the identification of continuous-time fractional order linear systems (FOLS) is investigated. In order to identify the differentiation or- ders as well as parameters and reduce the computation complexity, a novel identification method based on Chebyshev wavelet is proposed. Firstly, the Chebyshev wavelet operational matrices for fractional integration operator is derived. Then, the FOLS is converted to an algebraic equation by using the the Chebyshev wavelet operational matrices. Finally, the parameters and differentiation orders are estimated by minimizing the error between the output of real system and that of identified systems. Experimental results show the effectiveness of the proposed method.

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