Transfer-function and kernel inconsistencies in a 2016 paper of Caputo and Fabrizio

This independent technical comment examines specified transform identities in Caputo and Fabrizio, Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels, Progress in Fractional Differentiation and Applications 2(1) (2016), 1–11, DOI: 10.18576/pfda/020101. It derives the rational transfer function, corrected frequency response, and causal impulse kernel; supplies explicit counterchecks; and identifies inconsistencies in the diffusion and spatial Gaussian calculations. The source archive includes a standard-library Python verification script. This is not an official publisher corrigendum and has not been peer reviewed. The findings support corrections to specified formulas and do not establish inadmissibility of every model or recommend retraction. AI assistance: An AI assistant was used for English improvement, numerical and algebraic checks, and assistance with mathematical analysis and drafting. The author bears full responsibility for the construction and correctness of the counterexamples, theorems, and proofs, and for all definitions, references, and conclusions.