On a connection between powers of operators and fractional Cauchy problems |
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Authors: | Valentin Keyantuo Carlos Lizama |
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Institution: | 1. Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico, P.O. Box 70377, San Juan, PR, 00936-8377, USA 2. Departamento de Matem??tica, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile
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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. |
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