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
Description
Summary: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 $r\in \mathbb{R}$.
ISSN:1687-1847

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