# Laplace transform of some special functions in terms of generalized Meijer $G$-functions

Volume 15, Issue 2, pp 109--122
Publication Date: September 17, 2021 Submission Date: June 09, 2021 Revision Date: July 16, 2021 Accteptance Date: July 26, 2021
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### 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.

### Share and Cite

##### 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

### Keywords

• Meijer $G$-functions
• generalized Meijer $G$-functions
• Laplace transform
• generalized hypergeometric functions
• generalized Bessel functions

•  33C60
•  44A10
•  33C20
•  33C10