970 resultados para Fractional Laplace and Dirac operators


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"AEC Contract AT(04-3)-400."

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Includes bibliography.

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∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

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An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type.

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We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

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Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.

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Mathematics Subject Classification: 47A56, 47A57,47A63