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.
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Carlos Lizama partially supported by Fondecyt grant 1100485.
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Keyantuo, V., Lizama, C. On a connection between powers of operators and fractional Cauchy problems. J. Evol. Equ. 12, 245–265 (2012). https://doi.org/10.1007/s00028-011-0131-1
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DOI: https://doi.org/10.1007/s00028-011-0131-1