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.
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American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1)
This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics |
| DOI | 10.11648/j.ajtas.s.2017060501.20 |
| Page(s) | 66-70 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
Optimal Control, Fractional Order System, Expansion Formula for Fractional Derivative, Parabolic Partial Differential Equations, Functional Analysis, Interior and Neumann Boundary Controls
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APA Style
Mahmoud M. El-borai, Mohamed A. Abdou, Mai Taha Elsayed. (2017). Optimal Control of a Class of Parabolic Partial Fractional Differential Equations. American Journal of Theoretical and Applied Statistics, 6(5-1), 66-70. https://doi.org/10.11648/j.ajtas.s.2017060501.20
ACS Style
Mahmoud M. El-borai; Mohamed A. Abdou; Mai Taha Elsayed. Optimal Control of a Class of Parabolic Partial Fractional Differential Equations. Am. J. Theor. Appl. Stat. 2017, 6(5-1), 66-70. doi: 10.11648/j.ajtas.s.2017060501.20
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Download@article{10.11648/j.ajtas.s.2017060501.20,
author = {Mahmoud M. El-borai and Mohamed A. Abdou and Mai Taha Elsayed},
title = {Optimal Control of a Class of Parabolic Partial Fractional Differential Equations},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {5-1},
pages = {66-70},
doi = {10.11648/j.ajtas.s.2017060501.20},
url = {https://doi.org/10.11648/j.ajtas.s.2017060501.20},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2017060501.20},
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.},
year = {2017}
}
TY - JOUR T1 - Optimal Control of a Class of Parabolic Partial Fractional Differential Equations AU - Mahmoud M. El-borai AU - Mohamed A. Abdou AU - Mai Taha Elsayed Y1 - 2017/08/09 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.s.2017060501.20 DO - 10.11648/j.ajtas.s.2017060501.20 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 66 EP - 70 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.s.2017060501.20 AB - 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. VL - 6 IS - 5-1 ER -
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