Title: Analysis of the bilateral Laplace transform on time scales with applications

Authors: Tom Cuchta; Svetlin Georgiev

Addresses: Department of Computer Science and Math, Fairmont State University, Fairmont,WV 26554, USA ' Department of Mathematics, Sorbonne University, Paris, 75006, France

Abstract: The bilateral Laplace transform on time scales is investigated analytically and its absolute convergence, uniform convergence, and inversion integral are proven. Afterwards, a Fourier transform is defined and used to solve partial dynamic equations.

Keywords: time scales calculus; bilateral Laplace transform; Fourier transform; Hilger complex plane; Hilger circle; exponential order; region of convergence; first order partial dynamic equation; second order partial dynamic equation.

DOI: 10.1504/IJDSDE.2021.117356

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.255 - 274

Received: 07 Apr 2020
Accepted: 14 Jul 2020

Published online: 12 Aug 2021 *

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