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

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

Published:2018-12-19 Issue:7-8 Volume:19 Page:753-761
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
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Author:

Zhou Y.¹²,Manimaran J.³,Shangerganesh L.³,Debbouche A.⁴

Affiliation:

1. Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R. China

2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

3. Department of Humanities and Sciences, National Institute of Technology, Farmagudi, Ponda, Goa 403 401, India

4. Department of Mathematics, Guelma University, Guelma24000, Algeria

Abstract

AbstractWe 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2018-0035/pdf

Reference76 articles.

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