A Generalized Approach of Triple Integral Transforms and Applications

Abstract

In this study, we introduce a novel generalization of triple integral transforms, which is called a general triple transform. We present the definition of the new approach and prove the main properties related to the existence, uniqueness, shifting, scaling, and inverse. Moreover, relations between the new general triple transform and other transforms are presented, and new results related to partial derivatives and the triple convolution theorem are established. We apply the general triple transform to solve some applications of various types of partial differential equations. The strength of the new approach is that it covers almost all integral transforms of order one, two, and three, and hence no need to find new formulas of triple integral transforms or to study the basic properties.