A definition for the Laplace transform corresponding to the nabla difference operator is given. Several properties of this Laplace transform are established. Further, a definition for the discrete nabla Mittag-Leffler function is provided. Our results are then shown to be robust enough to lead to a practical method for solving initial value problems for discrete fractional nabla difference equations of order υ, 0 < υ <1.
|Original language||English (US)|
|Number of pages||19|
|Journal||Panamerican Mathematical Journal|
|State||Published - Jul 1 2011|
- Laplace transform
- Mittag-Leffler function
- Nabla-difference operator