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Displaying similar documents to “The fractional Langevin equation: Brownian motion revisited.”

Inverse Problem for Fractional Diffusion Equation

Tuan, Vu Kim (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30 We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral...

On a 3D-Hypersingular Equation of a Problem for a Crack

Samko, Stefan (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 45DB05, 45E05, 78A45 We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.