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

Rafeiro, Humberto; Samko, Stefan

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 4, page 399-421
- ISSN: 1311-0454

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topRafeiro, 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 -

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