On a connection between powers of operators and fractional Cauchy problems (Q692823)
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scientific article; zbMATH DE number 6113149
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a connection between powers of operators and fractional Cauchy problems |
scientific article; zbMATH DE number 6113149 |
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On a connection between powers of operators and fractional Cauchy problems (English)
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6 December 2012
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The paper is devoted to connections between ordinary non-homogeneous equations and fractional abstract Cauchy problems (FACP) on Banach spaces. In particular, by using the subordination principle, the authors provide an explicit form of the common solution involving special functions whenever the domination operator of FACP is the generator of a \(C_0\)-semigroup. Some illustrations of the main result are also given at the end of the paper.
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perturbed fourth order PDEs
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Cauchy problem
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iterated Brownian motion
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Caputo derivative
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\(C_0\)-semigroups
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PDE connection
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\(\alpha\)-resolvent families
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Wright function
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