Identifying an unknown time-dependent boundary source in time-fractional diffusion equation with a non-local boundary condition

This paper is devoted to determining a time-dependent factor of an unknown source on some subboundary conditions for a time-fractional diffusion equation from the non-local measurement data. We prove existence and uniqueness of the solution of the inverse boundary source by using the Lax-Milgram Lemma in some suitable Sobolev spaces. Consequently, we use the profitable meshless method based on radial basis functions to solve the inverse problem. The numerical experimental results and numerical simulations show that the proposed scheme is effective and stable when one considers measurements input data contaminated with noise. (C) 2019 Elsevier B.V. All rights reserved.