Modified Laplace transform and its properties

Volume 21, Issue 2, pp 127--135 http://dx.doi.org/10.22436/jmcs.021.02.04

Publication Date: April 06, 2020 Submission Date: September 04, 2019 Revision Date: October 14, 2019 Accteptance Date: March 03, 2020

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Authors

Mohd Saif - Department of Applied Mathematics, Aligarh Muslim University, Aligarh-202002, India. Faisal Khan - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Kottakkaran Sooppy Nisar - Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, 11991, Saudi Arabia. Serkan Araci - Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410, Gaziantep, Turkey.

Abstract

In this paper we propose a new definition of the modified Laplace transform \(\mathcal{L}_{a}(f(t))\) for a piece-wise continuous function of exponential order which further reduces to simple Laplace transform for \(a=e\) where \(a\neq1\) and \(a>0.\) Also we prove some basic results of this modified Laplace transform and connection with different functions.

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Keywords

• Laplace transform
• convolution
• double Laplace transform

MSC

•  44A10
•  44A35
•  44A30

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