TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=80051681503&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051681503&partnerID=8YFLogxK
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 -