Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions

Volume 15, Issue 2, pp 109--122 http://dx.doi.org/10.22436/jnsa.015.02.03
Publication Date: September 17, 2021 Submission Date: June 09, 2021 Revision Date: July 16, 2021 Accteptance Date: July 26, 2021

Authors

S. A. H. Shah - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. S. Mubeen - Department of Mathematics, University of Sargodha, Sargodha, Pakistan.


Abstract

The aim of this paper is to prove Laplace transform of some special functions in term of generalized Meijer \(G\)-functions. Some properties of generalized Meijer \(G\)-functions will be discussed. We investigate the Laplace transform of different hypergeometric functions in the form of generalized Meijer \(G\)-functions and hypergeometric functions. We derive Laplace transform of Bessel \(k\)-functions, hyper-Bessel \(k\)-functions, incomplete gamma \(k\)-function, sine \(k\)-integral, sine hyperbolic \(k\)-integral, Kelvin \(k\)-function in the form of generalized Meijer \(G\)-functions. In fact, we provide new approach to find Laplace transform of said functions.


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ISRP Style

S. A. H. Shah, S. Mubeen, Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions, Journal of Nonlinear Sciences and Applications, 15 (2022), no. 2, 109--122

AMA Style

Shah S. A. H., Mubeen S., Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions. J. Nonlinear Sci. Appl. (2022); 15(2):109--122

Chicago/Turabian Style

Shah, S. A. H., Mubeen, S.. "Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions." Journal of Nonlinear Sciences and Applications, 15, no. 2 (2022): 109--122


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