(2016). THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI. test, 7(1), 12-23. doi: 10.21608/jfca.2023.308277
. "THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI". test, 7, 1, 2016, 12-23. doi: 10.21608/jfca.2023.308277
(2016). 'THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI', test, 7(1), pp. 12-23. doi: 10.21608/jfca.2023.308277
THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI. test, 2016; 7(1): 12-23. doi: 10.21608/jfca.2023.308277

THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI

Journal of Fractional Calculus and Applications
Volume 7, Issue 1, 2016, Pages 12-23    PDF (109.64 K)
DOI: 10.21608/jfca.2023.308277
Abstract
One of the problems in distribution theory is the lack of definitions of products and powers of distributions in general. In this paper, we choose a fixed δ-sequence without compact support and the generalized Taylor’s formula based on Caputo fractional derivatives to give meaning to the distributions δk(x) and (δ′)k(x) for some values of k. These can be regarded as powers of
Dirac delta functions.
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