American Journal of Theoretical and Applied Statistics

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Optimal Control of a Class of Parabolic Partial Fractional Differential Equations

Received: 28 July 2017    Accepted: 31 July 2017    Published: 9 August 2017
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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.

DOI 10.11648/j.ajtas.s.2017060501.20
Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1, September 2017)

This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics

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.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Optimal Control, Fractional Order System, Expansion Formula for Fractional Derivative, Parabolic Partial Differential Equations, Functional Analysis, Interior and Neumann Boundary Controls

References
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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

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    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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    AMA 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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  • @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}
    }
    

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    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
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    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    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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Author Information
  • Faculty of Science, Alexandria University, Alexandria, Egypt

  • Faculty of Education, Alexandria University, Alexandria, Egypt

  • Faculty of Education, Alexandria University, Alexandria, Egypt

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