On a time–space fractional backward diffusion problem with inexact orders

In this paper, we focus on the backward diffusion problem with the Caputo fractional derivative operator in time and a general spatial nonlocal operator. For T>0 and s∈[0,T), we consider the problem (Ps) of recovering the distribution u(x,s) from a measure of the final data u(x,T) for the following non-homogeneous time–space fractional diffusion equation Dtαu(x,t)+KβLγu(x,t)=f(x,t)inRn×(0,T)subject to the final condition u(x,T)=uT(x)inRn. The derivative orders and the nonlocal operator are perturbed with noises. Firstly, for 0