Control and numerical approximation of fractional diffusion equations

The aim of this chapter is to give a broad panorama the control properties fractional diffusive models from numerical analysis and simulation perspective. We do by surveying several research results we obtained in last years, focusing particular on computation controls, though not forgetting recall other relevant contributions which can be currently found literature prolific field. Our reference model will non-local dynamics driven Laplacian bounded domain Ω. starting point our Finite Element approximation for associated elliptic one two space-dimensions, also present error estimates convergence rates L2 energy norm. Secondly, address specific scenarios: firstly, consider standard interior problem, acting small subset ω⊂Ω. move attention exterior region O⊂Ωc located outside This notion extends boundary framework, nature does allow controls supported ∂Ω. conclude discussing interesting problem simultaneous control, families parameter-dependent heat equations at designing unique function capable steering all different realizations same target configuration. In see how employment stochastic optimization techniques may help alleviating computational burden controls. discussion complemented open problems related with are unsolved interest future investigation.