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Fractional abstract Cauchy problems. (English) Zbl 1242.34008
Fractional abstract Cauchy problems with order \(\alpha \in (1,2)\) are studied. Existence and uniqueness of mild solutions and strong solutions of the inhomogeneous fractional Cauchy problem are established.

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
47D06 One-parameter semigroups and linear evolution equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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