Solving Partial Integro-Differential Equations via Double Formable Transform

In this study, we present a new double integral transform called the double formable transform. Several properties and theorems related to existing conditions, partial derivatives, the double convolution theorem, and others are presented. Additionally, we use a convolution kernel to solve linear partial integro-differential equations (PIDE) by using the double formable transform. By solving numerous cases, the double formable transform’s ability to turn the PIDE into an algebraic equation that is simple to solve is demonstrated.