A new exponential type Kernel integral transform: Khalouta transform and its applications

Abstract

In this paper, we suggest a new integral transform called the Khalouta transform, which is a generalization of many integral transforms having exponential type kernel. We discuss certain results on the inverse and the existence of this integral transform. We present useful properties of the Khalouta transform and their applications to solve differential equations. Furthermore, we prove the duality between the Khalouta transform and other transforms such as the Laplace-Carson transform, Sumudu transform, ZZ transform, ZMA transform, Elzaki transform, Aboodh transform, Natural transform and Shehu transform. Finally, we ensure the efficiency and accuracy of the Khalouta transform by solving various examples of both ordinary, integro and partial differential equations.