Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems

This article investigates a space–time fractional diffusion equation with a nonlinear source and a space nonlocal operator. The well-posedness is demonstrated from using contraction mapping theorem and generalized Gronwall's inequality firstly. Based on the forward problem, we prove that a nonlinear source term and a fractional order of time derivative are uniquely determined by data which can be observed at one fixed spatial point.