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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/35842

Title: Maximum principles for time-fractional Cauchy problems with spatially non-local components
Authors: Biswas, Anup
Lorinczi, Jozsef
Issue Date: 2019
Publisher: De Gruyter
Citation: BISWAS, A. and LORINCZI, J., 2019. Maximum principles for time-fractional Cauchy problems with spatially non-local components. Fractional Calculus and Applied Analysis, In Press.
Abstract: We 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.
Description: This paper is in closed access until 12 months after publication.
Sponsor: This research of AB was supported in part by an INSPIRE faculty fellowship and a DST-SERB grant EMR/2016/004810.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/35842
Publisher Link: https://www.degruyter.com/view/j/fca
ISSN: 1311-0454
Appears in Collections:Closed Access (Maths)

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