A comment on a controversial issue: A generalized fractional derivative cannot have a regular kernel
2020 ◽
Vol 23
(1)
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pp. 211-223
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Keyword(s):
AbstractThe problem whether a given pair of functions can be used as the kernels of a generalized fractional derivative and the associated generalized fractional integral is reduced to the problem of existence of a solution to the Sonine equation. It is shown for some selected classes of functions that a necessary condition for a function to be the kernel of a fractional derivative is an integrable singularity at 0. It is shown that locally integrable completely monotone functions satisfy the Sonine equation if and only if they are singular at 0.
2004 ◽
Vol 53
(2)
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pp. 369-386
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Keyword(s):
2013 ◽
Vol 59
(6)
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pp. 3922-3931
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Keyword(s):
2008 ◽
Vol 45
(4)
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pp. 940-952
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2020 ◽
Vol 54
(1 (251))
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pp. 35-43
Keyword(s):
2012 ◽
Vol 437
(2)
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pp. 601-611
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2016 ◽
Vol 19
(5)
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