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Maximum principles for time-fractional Cauchy problems with spatially non-local components

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journal contribution
posted on 2018-11-08, 14:48 authored by Anup Biswas, Jozsef Lorinczi
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.

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 Analysis

Volume

21

Issue

5

Pages

1335-1359

Citation

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 Gruyter

Version

  • 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-2018-0070

Acceptance date

2018-11-03

Publication date

2019-01-13

Copyright date

2019

ISSN

1311-0454

eISSN

1314-2224

Language

  • en

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