Maximal Regularity for Fractional Cauchy Equation in Hölder Space and Its Approximation-Reference-Cited by-同舟云学术

Maximal Regularity for Fractional Cauchy Equation in Hölder Space and Its Approximation

Published:2019-01-30 Issue:4 Volume:19 Page:779-796
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Liu Li¹,Fan Zhenbin¹,Li Gang¹,Piskarev Sergey²

Affiliation:

1. School of Mathematical Sciences , Yangzhou University , Yangzhou, Jiangsu 225002 , P. R. China

2. Scientific Research Computer Center , Lomonosov Moscow State University , Leninskie Gory , Moscow 119899 , Russia

Abstract

Abstract We derive the well-posedness and maximal regularity of the fractional Cauchy problem in Hölder space C 0 γ ⁢ ( E )

{C_{0}^{\gamma}(E)}

. We also obtain the existence and stability of new implicit difference schemes for the general approximation to the nonhomogeneous fractional Cauchy problem. Our analysis is based on the approaches of the theory of β-resolvent families, functional analysis and numerical analysis.

Funder

National Natural Science Foundation of China

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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