A Memoir on Pseudo-Variational Techniques for Parabolic PDE’s Incorporating Boundary Value Constraints

To enrich existing literature and extend the reach of relevant apt theoretical techniques, an alternative for proxy pseudo-variational analysis of a fundamental class of parabolic Partial Differential Equations (PDE’s) is brought to the fore in this paper. Classical results in Sobolev Space theory are extrapolated with the aid of more current, standard tools from developments in fractional calculus. The high potency of inference from data obtained via the trace boundary operator is proffered, with the simple heat equation in one spatial dimension as a case study.