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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/1389787 |
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| _version_ | 1832560227552067584 |
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| author | Abd-Allah Hyder M. EL-Badawy |
| author_facet | Abd-Allah Hyder M. EL-Badawy |
| author_sort | Abd-Allah Hyder |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-15129ffb7ff349f5a32c9c908229e1fa |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-15129ffb7ff349f5a32c9c908229e1fa2025-02-03T01:28:04ZengWileyJournal 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 |
| spellingShingle | Abd-Allah Hyder M. EL-Badawy Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator Journal of Function Spaces |
| title | 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_short | Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator |
| title_sort | distributed control for time fractional differential system involving schrodinger operator |
| url | http://dx.doi.org/10.1155/2019/1389787 |
| work_keys_str_mv | AT abdallahhyder distributedcontrolfortimefractionaldifferentialsysteminvolvingschrodingeroperator AT melbadawy distributedcontrolfortimefractionaldifferentialsysteminvolvingschrodingeroperator |