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Weakness and Mittag–Leffler Stability of Solutions for Time-Fractional Keller–Segel Models

  • Y. Zhou , J. Manimaran , L. Shangerganesh and A. Debbouche EMAIL logo
Published/Copyright: August 22, 2018

Abstract

We introduce a time-fractional Keller–Segel model with Dirichlet conditions on the boundary and Caputo fractional derivative for the time. The main result shows the existence theorem of the proposed model using the Faedo–Galerkin method with some compactness arguments. Moreover, we prove the Mittag–Leffler stability of solutions of the considered model.

MSC 2010: 35R11; 34A08; 35B35; 35D30

Acknowledgements:

The project of first author is supported by National Natural Science Foundation of China (11671339). The work of the third author is supported by the DST-SERB Early Career Award File No. ECR/20l6/000624.

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Received: 2018-02-04
Published Online: 2018-08-22
Published in Print: 2018-12-19

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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