A parametrix construction for time-fractional partial differential equations

2026/07/30 by Sandro Coriasco, Giovanni Girardi, Stevan Pilipović
Mathematics · #math.AP #msc:35A17 #msc:35S10 #msc:47G30 #msc:35S05 #msc:44A10

paper · pdf

18 pages. Materials originally included in the first version of arXiv:2511.04885

arxiv created 2026/07/30 · arxiv updated 2026/07/31

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.

Citations

• Representation formula, regularity, and decay of solutions for sub-diffusion equations
• Positivity of the fundamental solution for fractional diffusion and wave\n equations
• Time-fractional equations with reaction terms: fundamental solutions and asymptotics
• Solution theory to Semilinear Hyperbolic Stochastic Partial Differential Equations with polynomially bounded coefficients

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