In this paper, we study two new methods for approximating the viability kernel of a given set for a Holderian differential inclusion. We approximate this kernel by viability kernels for discrete dynamical systems. We prove a convergence result when the differential inclusion is replaced by a sequence of recursive inclusions. Furthermore, when the given set is approached by a sequence of suitable finite sets, we prove our second main convergence result. This paper is the first step to obtain numerical methods
