Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives. (English) Zbl 1266.47066

Li, Kexue; Peng, Jigen; Jia, Junxiong

J. Funct. Anal. 263, No. 2, 476-510 (2012).

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.

Reviewer: Juan J. Trujillo (La Laguna)

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

Keywords:

Riemann-Liouville fractional derivative; fractional resolvent; well-posedness; Cauchy problem

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