An analytic semigroup generated by a fractional differential operator
Analysis of PDEs
2019-09-19 v2
Abstract
We study a space-fractional diffusion problem, where the non-local diffusion flux involves the Caputo derivative of the diffusing quantity. We prove the unique existence of regular solutions to this problem by means of the semigroup theory. We show that the operator defined as divergence of product of a positive function with the Caputo derivative is a generator of analytic semigroup.
Cite
@article{arxiv.1902.02818,
title = {An analytic semigroup generated by a fractional differential operator},
author = {Katarzyna Ryszewska},
journal= {arXiv preprint arXiv:1902.02818},
year = {2019}
}