Abstract:Using the spectral theory on the S-spectrum it is possible to define the fractional powers of a large class of vector operators. This possibility leads to new fractional diffusion and evolution problems that are of particular interest for nonhomogeneous materials where the Fourier law is not simply the negative gradient operator but it is a nonconstant coefficients differential operator of the formwhere, Ω can be either a bounded or an unbounded domain in R 3 whose boundary ∂Ω is considered suitably regular, Ω… Show more
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