Differential equations of fractional (that is, non-integer) order have in recent years proven to be very valuable tools for the modeling of many phenomena in science and engineering. Thus, there is a noticeable interest in theoretical and numerical results describing the properties of such equations and their solutions. This paper by Chen et al. is devoted to the investigation of certain theoretical questions in this context. Specifically, for a class of equations describing evolution processes, they provide sufficient conditions under which mild solutions (that is, weak solutions that satisfy an additional integrability condition) exist for all times.

The results are based on using methods from functional analysis. The paper should be of interest to researchers working on the theory of fractional differential equations and to scientists using models based on these equations to describe models with non-mathematical applications.