A parametrix construction for time-fractional partial differential equations
arXiv:2607.28028
The paper details how to build a parametrix for parameter‑dependent pseudodifferential operators that arise in time‑fractional partial differential equations, analyzing the parameter dependence of asymptotic terms, smoothing remainders, and related Laplace transforms of vector‑valued distributions.
Abstract
We prove in detail how to construct the parametrix of a parameter-dependent family of pseudodifferential operators, appearing in the analysis of time-fractional partial differential equations. In particular, we perform a precise study of the dependence from the parameter of the corresponding asymptotic expansion terms, as well as of the smoothing remainders. Moreover, we provide some results about the Laplace transform of vector-valued distributions, also appearing in the analysis of time-fractional partial differential equations.
18 pages. Materials originally included in the first version of arXiv:2511.04885