Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1323

 Title: On a Class of Fractional Type Integral Equations in Variable Exponent Spaces Authors: Rafeiro, HumbertoSamko, Stefan Keywords: Fractional IntegralsVariable Exponent Spaces1st Kind Integral EquationsSingular Integral EquationsGeneralized Abel EquationFredholmnessFractional Smoothness45A0545B0545E0545P0546E30 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 URI: http://hdl.handle.net/10525/1323 ISSN: 1311-0454 Appears in Collections: 2007

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