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- W2890637143 abstract "This paper is devoted to the inverse generator problem in the setting of generators of integrated resolvent operator functions. It is shown that if the operator A is the generator of a tempered β-times integrated α-resolvent operator function ((α, β)-ROF) and it is injective, then the inverse operator A−1 is the generator of a tempered (α, γ)-ROF for all γ > β + 1/2, by means of an explicit representation of the integrated resolvent operator function based in Bessel functions of first kind. Analytic resolvent operator functions are also considered, showing that A−1 is in addition the generator of a tempered (δ, 0)-ROF for all δ < α. Moreover, the optimal decay rate of (α, β)-ROFs as t → ∞ is given. These result are applied to fractional Cauchy problem unsolved in the fractional derivative." @default.
- W2890637143 created "2018-09-27" @default.
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- W2890637143 date "2018-12-01" @default.
- W2890637143 modified "2023-10-03" @default.
- W2890637143 title "Inverses of generators of integrated fractional resolvent operator functions" @default.
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- W2890637143 doi "https://doi.org/10.1515/fca-2018-0081" @default.
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