Optimal Control of a Class of Parabolic Partial Fractional Differential Equations
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 5-1, September 2017, Pages: 66-70
Received: Jul. 28, 2017; Accepted: Jul. 31, 2017; Published: Aug. 9, 2017
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Authors
Mahmoud M. El-borai, Faculty of Science, Alexandria University, Alexandria, Egypt
Mohamed A. Abdou, Faculty of Education, Alexandria University, Alexandria, Egypt
Mai Taha Elsayed, Faculty of Education, Alexandria University, Alexandria, Egypt
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Abstract
In this paper, the existence of the solution of the parabolic partial fractional differential equation is studied and the solution bound estimate which are used to prove the existence of the solution of the optimal control problem in a Banach space is also studied, then apply the classical control theory to parabolic partial differential equation in a bounded domain with boundary problem. An expansion formula for fractional derivative, optimal conditions and a new solution scheme is proposed.
Keywords
Optimal Control, Fractional Order System, Expansion Formula for Fractional Derivative, Parabolic Partial Differential Equations, Functional Analysis, Interior and Neumann Boundary Controls
To cite this article
Mahmoud M. El-borai, Mohamed A. Abdou, Mai Taha Elsayed, Optimal Control of a Class of Parabolic Partial Fractional Differential Equations, American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics. Vol. 6, No. 5-1, 2017, pp. 66-70. doi: 10.11648/j.ajtas.s.2017060501.20
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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