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Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives. (English) Zbl 1266.47066
In this paper, the authors study certain Cauchy-type problems of fractional differential equations with fractional differential conditions, involving Riemann-Liouville derivatives, in infinite-dimensional Banach spaces. They introduce a certain fractional resolvent and study some of its properties. Moreover, they prove that a homogeneous \(\alpha\)-order Cauchy problem is well posed if and only if its coefficient operator is the generator of an \(\alpha\)-order fractional resolvent, and they give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of a certain inhomogeneous \(\alpha\)-order Cauchy problem.

MSC:
47D06 One-parameter semigroups and linear evolution equations
35R11 Fractional partial differential equations
34A08 Fractional ordinary differential equations and fractional differential inclusions
26A33 Fractional derivatives and integrals
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