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This article provides a comprehensive overview of the inverse source problem for a one-dimensional time-fractional diffusion equation with a potential term. The authors consider the Caputo derivative dtα as an operator from 0C1[0,T] to L2(0,T), and define the domain D(∂tα) as Hα(0,T). They propose an inverse source problem to uniquely determine f∈L2(0,T) by data y(x0,⋅) and (Jαy)x(x0,⋅), provided that ρ is given suitably.

The article is well written and provides clear explanations of its concepts and results. The authors provide sufficient evidence for their claims and present both sides of the argument equally. However, there are some points that could be improved upon in terms of trustworthiness and reliability. For example, while the authors discuss various nonlocal models in their introduction section, they do not provide any evidence or references to support their claims about these models' capabilities in describing anomalous diffusion. Additionally, while they discuss various assumptions required on boundary or initial time conditions for weak unique continuation in time-fractional diffusion equations in literature review section, they do not provide any evidence or references to support these claims either. Furthermore, while they discuss various Sobolev spaces used in their formulation of time-fractional derivatives in adequate Sobolev spaces section, they do not provide any evidence or references to support these claims either. Finally, while they discuss various assumptions made on p∈L∞ (0 , 1 ) , F ∈ L 2 ( 0 , T ; L 2 ( 0 , 1 ) ) , a ∈ L 2 ( 0