On the generalized fractional Laplace transform

Abstract

In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s
H
- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.