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Analyticity of solution operators to space-time fractional evolution equations

The abstract Cauchy problem for the space-time fractional evolution equation is considered, which contains the Caputo time-derivative of order β ∈ (0, 1) and the operator −Aα, α ∈ (0, 1), where −A generates a strongly continuous one-parameter semigroup on a Banach space. The analyticity of the solution operator is studied by applying subordination principles for space- and time-fractional evolution equations and taking into account the asymptotic behavior of the subordination kernels, expressed in terms of Levy extremal stable densities and Mainardi function.The abstract Cauchy problem for the space-time fractional evolution equation is considered, which contains the Caputo time-derivative of order β ∈ (0, 1) and the operator −Aα, α ∈ (0, 1), where −A generates a strongly continuous one-parameter semigroup on a Banach space. The analyticity of the solution operator is studied by applying subordination principles for space- and time-fractional evolution equations and taking into account the asymptotic behavior of the subordination kernels, expressed in terms of Levy extremal stable densities and Mainardi function.