New Laplace transforms for the generalized hypergeometric functions 2F2 and 3F3

Motivated by the new Laplace transforms for the Kummer’s confluent hypergeometric functions ${}_1{F}_1$ obtained recently by Kim et al. [Math $\mathrm{\&}$ Comput. Modelling, 55 (2012), pp. 1068–1071], the authors aim is to establish so far unknown Laplace transforms of rather general case of generalized hypergeometric functions ${}_2{F}_2(x)$ and ${}_3{F}_3(x)$ by employing extensions of classical summation theorems for the series ${}_2{F}_1$ and ${}_3{F}_2$ obtained recently by Kim et al. [Int. J. Math. Math. Sci., 309503, 26 pages, 2010]. Certain known results obtained earlier by Kim et al. follow cases of our main findings.