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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi


IMPACT FACTOR 2017: 1.162

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2191-0294
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Volume 19, Issue 7-8

Issues

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

Y. Zhou
  • Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R. China
  • Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
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/ J. Manimaran / L. Shangerganesh / A. Debbouche
Published Online: 2018-08-22 | DOI: https://doi.org/10.1515/ijnsns-2018-0035

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.

Keywords: fractional PDE; weak solution; Keller–Segel model; Faedo–Galerkin method; Mittag–Leffler stability

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

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About the article

Received: 2018-02-04

Published Online: 2018-08-22

Published in Print: 2018-12-19


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 753–761, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0035.

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