Solving Partial Integro Differential Equations Via Double ARA-Formable Transform

The double ARA-Formable transform is a novel double integral transform that we present in this research. Existence conditions, partial derivatives, the double convolution theorem, with other properties and theorems are discussed. Moreover, we solve linear partial integro-differential equations (PIDE) using a convolution kernel and the double ARA-Formable transform. We solve a significant number of examples and show that the double ARA-Formable transform converts the PIDE into a solvable algebraic equation.