Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Maximum principle for certain generalized time and space fractional diffusion equations


Authors: Ahmed Alsaedi, Bashir Ahmad and Mokhtar Kirane
Journal: Quart. Appl. Math. 73 (2015), 163-175
MSC (2010): Primary 35R11, 35B50
DOI: https://doi.org/10.1090/S0033-569X-2015-01386-2
Published electronically: January 29, 2015
MathSciNet review: 3322729
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Abstract: We present an inequality for fractional derivatives related to the Leibniz rule that not only answers positively a conjecture raised by J. I. Diaz, T. Pierantozi, and L. Vázquez but also helps us to obtain a modern proof of the maximum principle for fractional differential equations. The inequality turns out to be versatile in nature as it can be used to obtain a priori estimates for many fractional differential problems.


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Additional Information

Ahmed Alsaedi
Affiliation: Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Email: aalsaedi@kau.edu.sa

Bashir Ahmad
Affiliation: Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Email: bashirahmad_qau@yahoo.com

Mokhtar Kirane
Affiliation: Laboratoire de Mathématiques, Image et Applications, EA 3165, Université de La Rochelle, Pôle Sciences et Technologies, Avenue Michel Crépeau, 17000 La Rochelle, France, and Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Email: mkirane@univ-lr.fr

DOI: https://doi.org/10.1090/S0033-569X-2015-01386-2
Keywords: Maximum principle, time fractional differential equation, time and space fractional differential equation, fractional porous medium equation
Received by editor(s): April 11, 2013
Published electronically: January 29, 2015
Additional Notes: The third author is the corresponding author
Article copyright: © Copyright 2015 Brown University


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