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.
(2016). THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI. Journal of Fractional Calculus and Applications, 7(1), 12-23. doi: 10.21608/jfca.2023.308277
MLA
. "THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI", Journal of Fractional Calculus and Applications, 7, 1, 2016, 12-23. doi: 10.21608/jfca.2023.308277
HARVARD
(2016). 'THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI', Journal of Fractional Calculus and Applications, 7(1), pp. 12-23. doi: 10.21608/jfca.2023.308277
VANCOUVER
THE POWERS OF THE DIRAC DELTA FUNCTION BY CAPUTO FRACTIONAL DERIVATIVES C. K. LI. Journal of Fractional Calculus and Applications, 2016; 7(1): 12-23. doi: 10.21608/jfca.2023.308277
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