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

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

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 $r\in \mathbb{R}$.

Bibliographic Details
Main Authors:	Fahd Jarad, Yassine Adjabi, Dumitru Baleanu, Thabet Abdeljawad
Format:	Article
Language:	English
Published:	SpringerOpen 2018-11-01
Series:	Advances in Difference Equations
Subjects:	Conformable derivative Distribution Generalized functions Dirac delta function Delta sequence Galapon property
Online Access:	http://link.springer.com/article/10.1186/s13662-018-1865-7

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http://link.springer.com/article/10.1186/s13662-018-1865-7

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

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