✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.