On generalized distributions associated with singular partial differential operators

In this paper, we discuss various properties of the Riemann-Liouville operator over the generalized distributions $\mathcal{D}^{'}_w([0,+\infty[\times\mathbb{R})$ and other spaces. Next, we examine some properties of the convolution of the generalized distributions on the space $\mathcal{D}^{'}_w([0,+\infty[\times\mathbb{R})$.