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A study of the mathematical analysis - modelling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, and so on - involved in predicting complex mechanical/acoustical behaviour/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or of the boundary conditions, all of which are often affected by random perturbations, forms the class of related inverse or control problems.