An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control
In this study, we extend the investigations of fractional-order models of thermostats and guarantee the solvability of hybrid Caputo fractional models for heat controllers, satisfying some nonlocal hybrid multi-valued conditions with multi-valued feedback control, which involves the Chandrasekhar ke...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/10/759 |
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| author | Shorouk M. Al-Issa Ahmed M. A. El-Sayed Hind H. G. Hashem |
| author_facet | Shorouk M. Al-Issa Ahmed M. A. El-Sayed Hind H. G. Hashem |
| author_sort | Shorouk M. Al-Issa |
| collection | DOAJ |
| description | In this study, we extend the investigations of fractional-order models of thermostats and guarantee the solvability of hybrid Caputo fractional models for heat controllers, satisfying some nonlocal hybrid multi-valued conditions with multi-valued feedback control, which involves the Chandrasekhar kernel, by using hybrid Dhage’s fixed point theorem. A part of this study is dedicated to transforming this problem into an equivalent integral representation and then proving some existence results to achieve our aims. Furthermore, the continuous dependence of the unique solution on the control variable and on the set of selections will be discussed. Moreover, we provide an illustration to support our results. |
| first_indexed | 2024-03-10T21:14:15Z |
| format | Article |
| id | doaj.art-f3153d3d5de7487eaf424e79ff4b7e20 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T21:14:15Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f3153d3d5de7487eaf424e79ff4b7e202023-11-19T16:34:54ZengMDPI AGFractal and Fractional2504-31102023-10-0171075910.3390/fractalfract7100759An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback ControlShorouk M. Al-Issa0Ahmed M. A. El-Sayed1Hind H. G. Hashem2Department of Mathematics, Faculty of Arts and Sciences, International University of Beirut, Beirut 1107, LebanonDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria 21544, EgyptDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria 21544, EgyptIn this study, we extend the investigations of fractional-order models of thermostats and guarantee the solvability of hybrid Caputo fractional models for heat controllers, satisfying some nonlocal hybrid multi-valued conditions with multi-valued feedback control, which involves the Chandrasekhar kernel, by using hybrid Dhage’s fixed point theorem. A part of this study is dedicated to transforming this problem into an equivalent integral representation and then proving some existence results to achieve our aims. Furthermore, the continuous dependence of the unique solution on the control variable and on the set of selections will be discussed. Moreover, we provide an illustration to support our results.https://www.mdpi.com/2504-3110/7/10/759Caputo fractional derivativeheat controller modelmulti-valued boundary value problemsmulti-valued feedback control |
| spellingShingle | Shorouk M. Al-Issa Ahmed M. A. El-Sayed Hind H. G. Hashem An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control Fractal and Fractional Caputo fractional derivative heat controller model multi-valued boundary value problems multi-valued feedback control |
| title | An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control |
| title_full | An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control |
| title_fullStr | An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control |
| title_full_unstemmed | An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control |
| title_short | An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control |
| title_sort | outlook on hybrid fractional modeling of a heat controller with multi valued feedback control |
| topic | Caputo fractional derivative heat controller model multi-valued boundary value problems multi-valued feedback control |
| url | https://www.mdpi.com/2504-3110/7/10/759 |
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