On time-fractional partial differential equations of time-dependent piecewise constant order

被引：1

作者：

Kian, Yavar ^{[1
]}

Slodicka, Marian ^{[2
]}

Soccorsi, Eric ^{[3
]}

Van Bockstal, Karel ^{[4
]}

机构：

[1] Normandie Univ, Univ Rouen Normandy, CNRS, LMRS UMR, Rouen, France

[2] Univ Ghent, Dept Elect & Informat Syst, Res Grp Numer Anal & Math Modeling NaM2, Ghent, Belgium

[3] Aix Marseille Univ, Univ Toulon, CNRS, CPT, Marseille, France

[4] Univ Ghent, Ghent Anal & PDE Ctr, Dept Math Anal Log & Discrete Math, Ghent, Belgium

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年 / 48卷 / 02期

关键词：

anomalous diffusion; time-fractional partial derivative; time-dependent order; VARIABLE-ORDER; INTEGRODIFFERENTIAL EQUATION; NUMERICAL-METHODS;

D O I：

10.1002/mma.10439

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This contribution considers the time-fractional subdiffusion with a time-dependent variable-order fractional operator of order beta(t)$$ \beta (t) $$. It is assumed that beta(t)$$ \beta (t) $$ is a piecewise constant function with a finite number of jumps. A proof technique based on the Fourier method and results from constant-order fractional subdiffusion equations has been designed. This novel approach results in the well-posedness of the problem.

引用

页码：2354 / 2369

页数：16

共 42 条

[1] Adaptive discretization of an integro-differential equation with a weakly singular convolution kernel [J].