Abstract:
In this paper, we consider the Cauchy problem for fractional evolution equations with
the Caputo derivative. This problem is not well posed in the sense of Hadamard.
There have been many results on this problem when data is noisy in L2 and Hs
.
However, there have not been any papers dealing with this problem with observed
data in Lp with p = 2. We study three cases of source functions: homogeneous case,
inhomogeneous case, and nonlinear case. For all of them, we use a truncation
method to give an approximate solution to the problem. Under different assumptions
on the smoothness of the exact solution, we get error estimates between the
regularized solution and the exact solution in Lp. To our knowledge, Lp evaluations for
the inverse problem are very limited. This work generalizes some recent results on this problem