On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

Rafeiro, Humberto, and Samko, Stefan. "On a Class of Fractional Type Integral Equations in Variable Exponent Spaces." Fractional Calculus and Applied Analysis 10.4 (2007): 399-421. <http://eudml.org/doc/11334>.

@article{Rafeiro2007,
abstract = {2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized Abel equation, with f ∈ L^α,p(·), in dependence on the values of the variable exponent p(x) at the endpoints x = a and x = b.∗ This work was made under the project “Variable Exponent Analysis” supported by INTAS grant Nr.06-1000017-8792. * Supported by Fundação para a Ciência ea Tecnologia (FCT) (Grant No. SFRH / BD / 22977 / 2005), through Programa Operacional Ciência e Inovação 2010 (POCI2010) of the Portuguese Government, co-financed by the European Community Fund FSE.},
author = {Rafeiro, Humberto, Samko, Stefan},
journal = {Fractional Calculus and Applied Analysis},
keywords = {45A05; 45B05; 45E05; 45P05; 46E30},
language = {eng},
number = {4},
pages = {399-421},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On a Class of Fractional Type Integral Equations in Variable Exponent Spaces},
url = {http://eudml.org/doc/11334},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Rafeiro, Humberto
AU - Samko, Stefan
TI - On a Class of Fractional Type Integral Equations in Variable Exponent Spaces
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 4
SP - 399
EP - 421
AB - 2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized Abel equation, with f ∈ L^α,p(·), in dependence on the values of the variable exponent p(x) at the endpoints x = a and x = b.∗ This work was made under the project “Variable Exponent Analysis” supported by INTAS grant Nr.06-1000017-8792. * Supported by Fundação para a Ciência ea Tecnologia (FCT) (Grant No. SFRH / BD / 22977 / 2005), through Programa Operacional Ciência e Inovação 2010 (POCI2010) of the Portuguese Government, co-financed by the European Community Fund FSE.
LA - eng
KW - 45A05; 45B05; 45E05; 45P05; 46E30
UR - http://eudml.org/doc/11334
ER -