The Laplace transform on time scales revisited

DOI10.1016/j.jmaa.2006.10.089zbMath1120.44001OpenAlexW1997916828MaRDI QIDQ884375

Billy J. Jackson, Alice A. Ramos, Ian A. Gravagne, Robert J. II. Marks, John M. Davis

Publication date: 6 June 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.10.089

zbMATH Keywords

convolutioninversion formulatime scalestime scale Dirac delta functionaltime scale Laplace transform

Mathematics Subject Classification ID

Laplace transform (44A10) Discrete version of topics in analysis (39A12)

Related Items (21)

Singular value conditions for stability of dynamic switched systems ⋮ Bilateral Laplace transforms on time scales: convergence, convolution, and the characterization of stationary stochastic time series ⋮ Discrete complementary exponential and sine integral functions ⋮ LAPLACE-SUMUDU INTEGRAL TRANSFORM ON TIME SCALES ⋮ Itô's Lemma with quantum calculus (\(q\)-calculus): some implications ⋮ Exponentials and Laplace transforms on nonuniform time scales ⋮ Convergence of unilateral Laplace transforms on time scales ⋮ On multiple convolutions and time scales ⋮ A new integral transform on time scales and its applications ⋮ Integral transform methods for solving fractional dynamic equations on time scales ⋮ A generalized Fourier transform and convolution on time scales ⋮ A unified approach to high-gain adaptive controllers ⋮ Fractional Cauchy problem with Riemann-Liouville fractional delta derivative on time scales ⋮ Semigroups on time scales and applications to abstract Cauchy problems ⋮ An ergodic approach to Laplace transforms on time scales ⋮ On frequency distribution of impulsive feedback control times ⋮ Fractional Cauchy problem with Caputo nabla derivative on time scales ⋮ Fractional Cauchy problem with Riemann-Liouville derivative on time scales ⋮ Properties of the Laplace transform on time scales with arbitrary graininess ⋮ Further properties of the Laplace transform on time scales with arbitrary graininess ⋮ Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales

Cites Work

• Integration on time scales.
• A spectral characterization of exponential stability for linear time-invariant systems on time scales
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