Diagana, T.; Mophou, G. M.; N’guérékata, G. M. On the existence of mild solutions to some semilinear fractional integro-differential equations. (English) Zbl 1211.34094 Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 58, 17 p. (2010). Summary: This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution, we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for \(t > 0\) and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided. Cited in 27 Documents MSC: 34K30 Functional-differential equations in abstract spaces 34A08 Fractional ordinary differential equations 34K10 Boundary value problems for functional-differential equations Keywords:fractional abstract differential equation; sectorial operator PDFBibTeX XMLCite \textit{T. Diagana} et al., Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 58, 17 p. (2010; Zbl 1211.34094) Full Text: EMIS