[eng] In this paper we provide a concept of fuzzy partial metric space $(X,P,\ast)$ as an extension to fuzzy setting in the sense of Kramosil and Michalek, of the concept of partial metric due to Matthews. This extension has been defined using the residuum operator $\rightarrow_{\ast}$ associated to a continuous $t$-norm $*$ and without any extra condition on $*$. Similarly, it is defined the stronger concept of $GV$-fuzzy partial metric (fuzzy partial metric in the sense of George and Veeramani). After defining a concept of open ball in $(X,P,*)$, a topology $\mathcal{T}_{P}$ on $X$ deduced from $P$ is constructed, and it is showed that $(X,\T_P)$ is a $T_0$-space.