Laplace transforms for the nabla-difference operator

J. Hein; Z. McCarthy; N. Gaswick; B. McKain; Kaitlin Speer

Laplace transforms for the nabla-difference operator

J. Hein, Z. McCarthy, N. Gaswick, B. McKain, Kaitlin Speer

Research output: Contribution to journal › Article › peer-review

Abstract

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)
Pages (from-to)	79-97
Number of pages	19
Journal	Panamerican Mathematical Journal
Volume	21
Issue number	3
State	Published - Jul 1 2011

Keywords

Laplace transform
Mittag-Leffler function
Nabla-difference operator

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abstract = "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.",

keywords = "Laplace transform, Mittag-Leffler function, Nabla-difference operator",

author = "J. Hein and Z. McCarthy and N. Gaswick and B. McKain and Kaitlin Speer",

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AU - McCarthy, Z.

AU - Gaswick, N.

AU - McKain, B.

AU - Speer, Kaitlin

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Y1 - 2011/7/1

N2 - 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.

AB - 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.

KW - Laplace transform

KW - Mittag-Leffler function

KW - Nabla-difference operator

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Laplace transforms for the nabla-difference operator

Abstract

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