This article introduces an expansion of the triple Shehu transformation concept, extending it to the fourth order. Our approach begins by establishing the theoretical framework for these extended Shehu transformations, which we subsequently apply to obtain solutions for the fractional order partial differential equations within a three-dimensional context. It is important to note that the fractional derivatives in this study are considered in the Caputo sense. To illustrate the utility of our approach, we specifically focus on the fractional-order of the three-dimensional homogeneous heat equation. To present the resulting solution in a concise and elegant manner, we leverage the principles of Fox-function theory.