The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

Humberto Rafeiro; Makhmadiyor Yakhshiboev

doi:10.2478/s13540-011-0022-8

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

Humberto Rafeiro
, Makhmadiyor Yakhshiboev

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

After recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

Original language	English
Pages (from-to)	343-360
Number of pages	18
Journal	Fractional Calculus and Applied Analysis
Volume	14
Issue number	3
DOIs	https://doi.org/10.2478/s13540-011-0022-8
Publication status	Published - Sept 2011
Externally published	Yes

Keywords

Chen fractional integration
Marchaud fractional derivative
Riesz potentials
fractional integrals
variable exponent spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.2478/s13540-011-0022-8

Cite this

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abstract = "After recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.",

keywords = "Chen fractional integration, Marchaud fractional derivative, Riesz potentials, fractional integrals, variable exponent spaces",

author = "Humberto Rafeiro and Makhmadiyor Yakhshiboev",

note = "Funding Information: H. Rafeiro gratefully acknowledges financial support by Funda¸c{\~a}o para a Ci{\^e}ncia e a Tecnologia (FCT), Grant SFRH/BPD/63085/2009, Portugal.",

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T1 - The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

AU - Rafeiro, Humberto

AU - Yakhshiboev, Makhmadiyor

N1 - Funding Information: H. Rafeiro gratefully acknowledges financial support by Funda¸cão para a Ciência e a Tecnologia (FCT), Grant SFRH/BPD/63085/2009, Portugal.

PY - 2011/9

Y1 - 2011/9

N2 - After recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

AB - After recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

KW - Chen fractional integration

KW - Marchaud fractional derivative

KW - Riesz potentials

KW - fractional integrals

KW - variable exponent spaces

UR - https://www.scopus.com/pages/publications/80051681503

UR - https://www.scopus.com/pages/publications/80051681503#tab=citedBy

U2 - 10.2478/s13540-011-0022-8

DO - 10.2478/s13540-011-0022-8

M3 - Article

AN - SCOPUS:80051681503

SN - 1311-0454

VL - 14

SP - 343

EP - 360

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 3

ER -

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

Abstract

Keywords

ASJC Scopus subject areas

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