Phase‐Lag Integro‐Partial Differential Equation: Local and Nonlocal Solutions

Nonlocal information, such as material deformation, genetic genes, or the history of the disease, are essential as they provide us with additional details that increase the numerical solution’s accuracy. With the help of the phase delay, we may also predict the future of the phenomena we are researching. This study involves consideration of both the nonlocal conditions and the phase delay effect. The phase‐lag integro‐partial differential equation (I‐PDE) with nonlocal conditions is investigated in order to achieve this, transforming it into a two‐dimensional mixed integral equation (2‐D MIE). The I‐PDE, thus, has a unique solution, as shown by the Banach fixed point theorem. Furthermore, the solution’s convergence has been demonstrated using Picard’s approach. Since the obtained MIE equation requires a specific approach to find its solution. In this investigation, MIE is numerically addressed using the product Nyström method (PNM). Ultimately, numerical results were obtained by solving various types of applications. Therefore, many interesting conclusions were derived.