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

Abstract

Abstract 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 δr $\delta ^{r}$ and (δ′)r $(\delta^{\prime})^{r}$ for any r∈R $r\in \mathbb{R}$.

Keywords

• Conformable derivative
• Distribution
• Generalized functions
• Dirac delta function
• Delta sequence
• Galapon property