This paper is concerned with semilinear differential equations with nonlocal conditions in Banach spaces. Using the tools involving the measure of noncompactness and fixed point theory, existence of mild solutions is obtained without the assumption of compactness or equicontinuity on the associated linear semigroup.
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.… (More)