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Title: On a Class of Fractional Type Integral Equations in Variable Exponent Spaces
Authors: Rafeiro, Humberto
Samko, Stefan
Keywords: Fractional Integrals
Variable Exponent Spaces
1st Kind Integral Equations
Singular Integral Equations
Generalized Abel Equation
Fractional Smoothness
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 4, (2007), 399p-421p
Abstract: We 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.
Description: 2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30
ISSN: 1311-0454
Appears in Collections:2007

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