Evolutionary PDEs with Volterra Operators: Direct and Inverse Source Problems

Integro-differential problems arise in many practical situations when the solution of the governing PDE depends on its history. This is usually modelled by a Volterra operator. Such operators include also time-fractional derivatives, which are very in fashion in the last decades. Variable order fractional calculus represents a new direction in the research. There are still many open questions in this area, because the use of known techniques is very restricted. We try to point out the main difficulties, and we also state some open problems.