Existence and viability for fractional differential equations with initial conditions at inner points

This paper is concerned with nonlinear fractional differential equations with the Caputo derivative. Existence results are obtained for terminal value problems and initial value problems with initial conditions at inner points. It is also proved that the sufficient condition in order that a locally closed subset be a viable domain is the tangency condition. As a corollary, the existence of positive solutions is obtained. c ©2016 All rights reserved.