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

Li Liu, Zhenbin Fan, Gang Li and Sergey Piskarev

Abstract

We derive the well-posedness and maximal regularity of the fractional Cauchy problem in Hölder space C0γ(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.

MSC 2010: 34G10; 45L05; 65J10

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11571300

Award Identifier / Grant number: 11871064

Funding source: Russian Foundation for Basic Research

Award Identifier / Grant number: 17-51-53008

Award Identifier / Grant number: 16-01-00039

Funding statement: Zhenbin Fan was supported by the National Natural Science Foundation of China (Grant No. 11571300 and 11871064) and the High-Level Personnel Support Program of Yangzhou University. Gang Li was supported by the National Natural Science Foundation of China (Grant No. 11871064 and 11571300). Sergey Piskarev was supported by Russian Foundation for Basic Research (Grant No. 17-51-53008 and 16-01-00039).

Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions.

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Received: 2018-07-24
Revised: 2019-01-08
Accepted: 2019-01-14
Published Online: 2019-01-30
Published in Print: 2019-10-01

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