Maxwells equations and also the equations of fluid dynamics can be formulated as integral equations. These equations allow so called weak (non-differentiable) solutions, e.g. shock waves in fluid dynamics. That is why the integral equations are often seen as the more fundamental equations, see
Whatever physical model you choose, you have to understand that (the integral equation) is the real equation you care about, and (the partial differential equation) is just a convenient way to write the equation. https://math.stackexchange.com/a/3314745/27609
Absolutely nothing in physics is completely described by a PDE, if you look at a sufficiently small resolution, because space and time are not continuous. ... However almost everything in physics is described at a fundamental level by conservation laws which are most naturally expressed mathematically as integral equations not as differential equations. https://math.stackexchange.com/a/3315144/27609
However I have never seen an integral formulation of the equations of quantum mechanics (e.g. the Schrödinger equation) or an integral equation of Einsteins field equation of general relativity. So is there an integral formulation of QM or GR? And if not, why not? Are weak solutions not possible in QM and GR?