Properties of the Laplace transform on time scales with arbitrary graininess

DOI10.1080/10652469.2010.548335zbMath1236.44002OpenAlexW2126279832MaRDI QIDQ3107304

Başak Karpuz, Martin J. Bohner, Gusein Sh. Guseinov

Publication date: 23 December 2011

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2010.548335

zbMATH Keywords

Laplace transformexponential functiontime scalesdynamic equation

Mathematics Subject Classification ID

Laplace transform (44A10) Discrete version of topics in analysis (39A12) Difference equations, scaling ((q)-differences) (39A13) Real analysis on time scales or measure chains (26E70)

Related Items (19)

Li type oscillation theorem for delay dynamic equations ⋮ A Gompertz distribution for time scales ⋮ Asymptotic stability of the complex dynamic equation \(u^\Delta-z\cdot u+w\cdot u^\sigma=0\) ⋮ Delay dynamic equations on isolated time scales and the relevance of one‐periodic coefficients ⋮ The Bessel difference equation ⋮ The heat equation on time scales ⋮ Periodic functions related to the Gompertz difference equation ⋮ Discrete complementary exponential and sine integral functions ⋮ Exponentials and Laplace transforms on nonuniform time scales ⋮ A survey of recent results for the generalizations of ordinary differential equations ⋮ Integral transform methods for solving fractional dynamic equations on time scales ⋮ Analyticity of the complex time scale exponential ⋮ Volterra theory on time scales ⋮ An ergodic approach to Laplace transforms on time scales ⋮ Further properties of the Laplace transform on time scales with arbitrary graininess ⋮ Dynamic cobweb models with conformable fractional derivatives ⋮ Exact solution to a dynamic SIR model ⋮ Nonlinear dynamic equations on time scales with impulses and nonlocal conditions ⋮ On Volterra integral equations on time scales

Cites Work

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• The Laplace transform on isolated time scales
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• The \(h\)-Laplace and \(q\)-Laplace transforms
• The Laplace transform on time scales revisited
• Integration on time scales.
• A spectral characterization of exponential stability for linear time-invariant systems on time scales
• First and second order linear dynamic equations on time scales
• Oscillation results for a dynamic equation on a time scale

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