A NEW ∝-LAPLACE TRANSFORM ON TIME SCALES
By
Tukaram G.Thange1 and Sneha M. Chhatraband2
1Department of Mathematics, Yogeshwari Mahavidyalaya, Ambajogai, (M.S.), India-431517
2Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S.), India-431004
Email: tgthange@gmail.com, chhatrabandsneha@gmail.com
(Received: July 22, 2023, In format: August 31, 2023; Revised: September 24, 2023; Accepted: October 02, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53218
Abstract
In this paper we introduce a new ∝-Laplace transform which is a generalization of nabla version of Laplace transform on time scales. In particular for 0< ∝< 1 this transform will serve as fractional Laplace transform on time scales. Existence theorem and some important properties such as linearity, initial and nal value theorem, transform of integral, shifting theorem, transform of derivative are proved. Additionally convolution theorem and formulae for fractional integral, Riemann-Liouville fractional derivative, Liouville-Caputo fractional derivative, Mittag Leer function are given. At last for a suitable value of a fractional dynamic equation with given initial condition is solved.
2020 Mathematical Sciences Classification: 26E70, 44A35, 26A33
Keywords and Phrases: Time scales, Integral transform, Dynamic equations.