2020/05/09 by Yulong Li, Li, Yulong
Mathematics · #45E99 #46N20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Primary 26A33 #Secondary 34A08
paper · pdf · doi:10.48550/arxiv.2005.04405
openalex publication_date 2020/05/09 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28
This article provides techniques of raising the regularity of fractional order equations and resolves fundamental questions on the one-dimensional homogeneous boundary-value problem of skewed (double-sided) fractional diffusion advection reaction equation (FDARE) with variable coefficients on the bounded interval. The existence of the true (classical) solution together with norm estimation is established and the precise regularity bound is found; also, the structure of the solution is unraveled, capturing the essence of regularity, singularity, and other features of the solution. The key analysis lies in exploring the properties of Gauss hypergeometric functions, solving coupled Abel integral equations and dominant singular integral equations, and connecting the functions from fractional Sobolev spaces to the ones from Holderian spaces that admit integrable singularities at the endpoints.