Work

An anomalous fractional diffusion operator

Year: 2025

Type: article

Abstract: In this article, using that the fractional Laplacian can be factored into a product of the divergence operator, a Riesz potential operator and the gradient operator, we introduce an anomalous fractional diffusion operator, involving a matrix K ( x ), suitable when anomalous diffusion is being studied in a non homogeneous medium. For the case of K ( x ) a constant, symmetric positive definite matrix we show that the fractional Poisson equation is well posed, and determine the regularity of the solution in terms of the regularity of the right hand side function.

Source: Fractional Calculus and Applied Analysis

DOI: 10.1007/s13540-025-00394-5

Authors: Xiangcheng Zheng, V. J. Ervin, Hong Wang

Institutions: Shandong University, Clemson University, University of South Carolina

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590

Funders: National Science Foundation, Clemson University