In this paper, we investigate the existence of solutions to abstract boundary value problems of fractional differential equations on . The choice of the Banach space allows the solutions to be unbounded. Our approach mainly depends on the technique of Hausdorff measure of noncompactness in conjunction with the criterion of compactness in . Finally, an example in the Banach sequence space ℓ1 is given to illustrate our results.

The aim of this paper is to investigate the existence of weak solutions for a boundary value problem of a second order differential equation. As the main tool, we apply a Krasnosel'skii type fixed point theorem in conjunction with the technique of measures of weak noncompactness in Banach spaces. Finally, two examples are given to illustrate our abstract results. MSC: 35G30; 47H08; 47H09