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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 differential equations 26A33 Fractional derivatives and integrals (real functions)
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