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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title = "Laplace transforms for the nabla-difference operator",

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 - Hein, J.

AU - McCarthy, Z.

AU - Gaswick, N.

AU - McKain, B.

AU - Speer, Kaitlin

PY - 2011/7/1

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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UR - https://www.scopus.com/pages/publications/80055086056#tab=citedBy

M3 - Article

AN - SCOPUS:80055086056

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EP - 97

JO - Panamerican Mathematical Journal

JF - Panamerican Mathematical Journal

IS - 3

ER -

Laplace transforms for the nabla-difference operator

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