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Fractional diffusion on bounded domains. (English) Zbl 1488.35557

Summary: The mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. This paper discusses the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

MSC:

35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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