Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator

Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator

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 uniquene...

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Main Authors: Abd-Allah Hyder, M. EL-Badawy
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2019/1389787
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spelling doaj-15129ffb7ff349f5a32c9c908229e1fa2020-11-25T00:40:30ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/13897871389787Distributed Control for Time-Fractional Differential System Involving Schrödinger OperatorAbd-Allah Hyder0M. EL-Badawy1King Khalid University, College of Science, Department of Mathematics, P.O. Box 9004, 61413 Abha, Saudi ArabiaMathematics Department, Al-Azhar University, Nasr City, Cairo, EgyptIn 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.http://dx.doi.org/10.1155/2019/1389787
collection DOAJ
language English
format Article
sources DOAJ
author Abd-Allah Hyder
M. EL-Badawy
spellingShingle Abd-Allah Hyder
M. EL-Badawy
Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
Journal of Function Spaces
author_facet Abd-Allah Hyder
M. EL-Badawy
author_sort Abd-Allah Hyder
title Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
title_short Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
title_full Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
title_fullStr Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
title_full_unstemmed Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator
title_sort distributed control for time-fractional differential system involving schrödinger operator
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2019-01-01
description 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.
url http://dx.doi.org/10.1155/2019/1389787
work_keys_str_mv AT abdallahhyder distributedcontrolfortimefractionaldifferentialsysteminvolvingschrodingeroperator
AT melbadawy distributedcontrolfortimefractionaldifferentialsysteminvolvingschrodingeroperator
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