Journal
APPLIED MATHEMATICS LETTERS
Volume 22, Issue 11, Pages 1659-1664Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2009.05.011
Keywords
Fractional derivative; Fractional Taylor's series; Mittag-Leffler function; Fractional transform; Laplace's transform
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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. (C) 2009 Elsevier Ltd. All rights reserved.
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