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Journal of Function Spaces Volume 2019 ,2019-07-22
Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
Research Article
Abd-Allah Hyder 1 , 2 M. EL-Badawy 3
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DOI:10.1155/2019/1389787
Received 2019-03-06, accepted for publication 2019-06-18, Published 2019-06-18
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摘要

In this paper, we investigate the distributed optimal control problem for time-fractional differential system involving Schrödinger operator defined on Rn. The time-fractional derivative is considered in the Riemann-Liouville sense. By using the Lax-Milgram lemma, we prove the existence and uniqueness of the solution of this system. For the fractional Dirichlet problem with linear quadratic cost functional, we give some equations and inequalities which provide the necessary and sufficient optimality conditions. Moreover, we provide specific application examples to demonstrate the effectiveness of our results.

授权许可

Copyright © 2019 Abd-Allah Hyder and M. EL-Badawy. 2019
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

通讯作者

Abd-Allah Hyder.King Khalid University, College of Science, Department of Mathematics, P.O. Box 9004, 61413 Abha, Saudi Arabia, kku.edu.sa;Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt, azhar.edu.eg.abahahmed@kku.edu.sa

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Abd-Allah Hyder,M. EL-Badawy. Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator. Journal of Function Spaces ,Vol.2019(2019)

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