Open Access
Jan 2017 Remarks on fractional derivatives of distributions*
Chenkuan Li, Changpin Li
Author Affiliations +
Tbilisi Math. J. 10(1): 1-18 (Jan 2017). DOI: 10.1515/tmj-2017-0001


This paper investigates a new approach to studying several fractional derivatives in the distributional sense based on the products of distributions and the delta sequence with compact support. Furthermore, we consider an asymptotic expression to the fractional derivative of the delta function and show that it is the first-order approximation in the Schwartz space. At the end of paper, we provide several asymptotic formulas to more complicated fractional derivatives of distributions.

Funding Statement

*This work is partially supported by NSFC under grant no. 11372170 and BURC.


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Chenkuan Li. Changpin Li. "Remarks on fractional derivatives of distributions*." Tbilisi Math. J. 10 (1) 1 - 18, Jan 2017.


Received: 12 October 2015; Accepted: 25 February 2016; Published: Jan 2017
First available in Project Euclid: 26 May 2018

zbMATH: 1358.46038
MathSciNet: MR3607263
Digital Object Identifier: 10.1515/tmj-2017-0001

Primary: 46F10
Secondary: 26A33

Keywords: convolution , delta function , distribution , first-order approximation , fractional derivative and Faà did Bruno formula , product

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

Vol.10 • No. 1 • Jan 2017
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