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Maximum principles for time-fractional Cauchy problems with spatially non-local components
journal contribution
posted on 2018-11-08, 14:48 authored by Anup Biswas, Jozsef LorincziWe show a strong maximum principle and an Alexandrov-Bakelman-Pucci estimate for the weak solutions of a Cauchy problem featuring Caputo time-derivatives and non-local operators in space variables given in terms of Bernstein functions of the Laplacian. To achieve this, first we propose a suitable meaning of a weak solution, show their existence and uniqueness, and establish a probabilistic representation in terms of time-changed Brownian motion. As an application, we also discuss an inverse source problem.
Funding
This research of AB was supported in part by an INSPIRE faculty fellowship and a DST-SERB grant EMR/2016/004810.
History
School
- Science
Department
- Mathematical Sciences
Published in
Fractional Calculus and Applied AnalysisVolume
21Issue
5Pages
1335-1359Citation
BISWAS, A. and LORINCZI, J., 2019. Maximum principles for time-fractional Cauchy problems with spatially non-local components. Fractional Calculus and Applied Analysis, 21(5), pp. 1335-1359.Publisher
De GruyterVersion
- AM (Accepted Manuscript)
Publisher statement
This paper was accepted for publication in the journal Fractional Calculus and Applied Analysis and the definitive published version is available at https://doi.org/10.1515/fca-2018-0070Acceptance date
2018-11-03Publication date
2019-01-13Copyright date
2019ISSN
1311-0454eISSN
1314-2224Publisher version
Language
- en