Inverse source problem in a space fractional diffusion equation from the final overdetermination

• DOI: 10.21136/am.2019.0251-18
• Publication Date: 2019-06-03T06:01:21Z
• Authors: Amir Hossein Sale...; Reza Bayat Tajvar; Alireza Ghanbari; Ali Safaie
• Keywords: 0101 mathematics; 01 natural sciences

t=T − ψ(x))2 dx is applied and shown that this cost functional is Frechet differentiable and its derivative can be formulated via the solution of an adjoint problem. In addition, Lipschitz continuity of the gradient is proved. These results help us to prove the monotonicity and convergence of the sequence {J′(f(n))}, where f(n) is the nth iteration of a gradient like method. At the end, the convexity of the Frechet derivative is given.