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.
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: 01 Sep 2021 *