On a connection between powers of operators and fractional Cauchy problems
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Abstract
Many phenomena in mathematical physics and in the theory of stochastic processes are recently described through fractional evolution equations. We investigate a general framework for connections between ordinary non-homogeneous equations in Banach spaces and fractional Cauchy problems. When the underlying operator generates a strongly continuous semigroup, it is known, using a subordination argument, that the fractional evolution equation is well posed. In this case, we provide an explicit form of the solution involving special functions, one example being the Airy function.
Mathematics Subject Classification (2000)
47D06 35C05 60J35 26A33 35K90 34G10Keywords
Perturbed fourth order PDEs Cauchy problem Iterated Brownian motion Caputo derivative C0-semigroups PDE connection α-Resolvent families Wright functionPreview
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