On defining the distributions δ r $\delta^{r}$ and ( δ ′ ) r $(\delta ^{\prime})^{r}$ by conformable derivatives

In this paper, starting from a fixed δ-sequence, we use the generalized Taylor’s formula based on conformable derivatives and the neutrix limit to find the powers of the Dirac delta function $\delta ^{r}$ and $(\delta^{\prime})^{r}$ for any $r\in \mathbb{R}$ .