• NEW IDENTITIES FOR LAPLACE TYPE INTEGRAL TRANSFORMS WITH APPLICATIONS

Abstract

In this work, the authors used Bromwich’s integral to derive a complex inversion formula for - transform and some new results related to Stieltjes and Widder – transforms. We give also new identities involving - transform and the new transforms. In this paper, the non - homogeneous partial fractional differential equation with non – constant coefficients defined in terms of Caputo derivatives is being solved via -integral transform.  Illustrative examples are also provided.