Simply because those natural disasters over recent years and their permanent risks, recently the environmental problems, and particularly the pollution problems have drawn increasing attention (Witherington and Martin in Understanding, assessing, and resolving light-pollution problems on sea turtle nesting beaches. Florida Marine Research Institute Technical Report, TR-2, 2000 [
9], Ge et al. in 55th conference on decision and control, Las Vegas, USA, 2016 [
7]). Moreover, we note that since the pollution problems are essentially due to the chemical or nuclear industries, etc., and one is worried about their expansion, the danger of pollution maybe increase when the pollution source remains unknown. As cited in El Jai and Afifi (Int J Appl Math Comput Sci 26(8):1447–1463, 1995) [
4], according to its nature (pointwise, zone, boundary, fixed, or moving), intensity, and life duration, a source can be characterized by several parameters. So the source can be regarded as an unknown control which is observed and detected via sensors
. In this chapter, we shall study the problem of regional detection
of unknown sources
for the Riemann–Liouville-type and Caputo-type time fractional diffusion systems
, which are considered as extensions of previous work (see El Jai and Afifi in Int J Appl Math Comput Sci 26(8):1447–1463, 1995 [
4], Afifi et al. in Int J Syst Sci 31(2):149-159, 2000 [
1], Afifi et al. in Int J Appl Math Comput Sci 11(2):319-348, 2001 [
2] for example).
