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Laplace’s transform of fractional order via the Mittag–Leffler function and modified Riemann–Liouville derivative

✍ Scribed by Guy Jumarie


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
375 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis


We propose a (new) definition of a fractional Laplace's transform, or Laplace's transform of fractional order, which applies to functions which are fractional differentiable but are not differentiable, in such a manner that they cannot be analyzed by using the Djrbashian fractional derivative. After a short survey on fractional analysis based on the modified Riemann-Liouville derivative, we define the fractional Laplace's transform. Evidence for the main properties of this fractal transformation is given, and we obtain a fractional Laplace inversion theorem.