Laplace transforms for the nabla-difference operator

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

    Research output: Contribution to journalArticlepeer-review

    32 Scopus citations

    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 languageEnglish (US)
    Pages (from-to)79-97
    Number of pages19
    JournalPanamerican Mathematical Journal
    Volume21
    Issue number3
    StatePublished - Jul 1 2011

    Keywords

    • Laplace transform
    • Mittag-Leffler function
    • Nabla-difference operator

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