BOUNDARY BEHAVIOUR OF POTENTIAL-TYPE INTEGRALS FOR THE MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATION
Abstract
We investigate the boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation (MTFDE) across the moving boundary. First, we establish the jump relation for the integral operator associated with the fundamental solution of the inhomogeneous MTFDE. Second, we prove the continuity of the integral operator generated by the kernel corresponding to the homogeneous MTFDE. Krasnoshchok obtained similar results for the time-fractional diffusion equation. However, in the multi-term case, the fundamental solution has more complex structure and does not admit standard scaling properties, which requires a different approach. Our results are essential for the analysis of boundary integral equations related to the MTFDE in time-dependent domains.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Differential Equations and Numerical Methods
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Journal of Integral Equations and Applications
- Publisher
- Rocky Mountain Mathematics Consortium
- Volume
- 38
- Issue
- 2
- Pages
- 201–220
- Publication date
- 16 July 2026
- Language
- EN