A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators
This article primarily focuses on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators. Two alternative sets of necessary requirements have been studied. In the first set, we use theories from functional analysis, the compactness of an asso...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/2/73 |
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| author | Velusamy Vijayakumar Kottakkaran Sooppy Nisar Dimplekumar Chalishajar Anurag Shukla Muslim Malik Ateq Alsaadi Saud Fahad Aldosary |
| author_facet | Velusamy Vijayakumar Kottakkaran Sooppy Nisar Dimplekumar Chalishajar Anurag Shukla Muslim Malik Ateq Alsaadi Saud Fahad Aldosary |
| author_sort | Velusamy Vijayakumar |
| collection | DOAJ |
| description | This article primarily focuses on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators. Two alternative sets of necessary requirements have been studied. In the first set, we use theories from functional analysis, the compactness of an associated resolvent operator, for our discussion. The primary discussion is proved in the second set by employing Gronwall’s inequality, which prevents the need for compactness of the resolvent operator and the standard fixed point theorems. Then, we extend the discussions to the fractional Sobolev-type semilinear integrodifferential systems. Finally, some theoretical and practical examples are provided to illustrate the obtained theoretical results. |
| first_indexed | 2024-03-09T21:56:11Z |
| format | Article |
| id | doaj.art-df2d8dfb9f0d411e8f9f57d78e6e8210 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:56:11Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-df2d8dfb9f0d411e8f9f57d78e6e82102023-11-23T19:58:46ZengMDPI AGFractal and Fractional2504-31102022-01-01627310.3390/fractalfract6020073A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent OperatorsVelusamy Vijayakumar0Kottakkaran Sooppy Nisar1Dimplekumar Chalishajar2Anurag Shukla3Muslim Malik4Ateq Alsaadi5Saud Fahad Aldosary6Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, IndiaDepartment of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Applied Mathematics, Virginia Military Institute (VMI) 435 Mallory Hall, Lexington, VA 24450, USADepartment of Applied Science, Rajkiya Engineering College Kannauj, Kannauj 209 732, Uttar Pradesh, IndiaSchool of Basic Sciences, Indian Institute of Technology, Mandi, Kamand 175 005, Himachal Pradesh, IndiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaThis article primarily focuses on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators. Two alternative sets of necessary requirements have been studied. In the first set, we use theories from functional analysis, the compactness of an associated resolvent operator, for our discussion. The primary discussion is proved in the second set by employing Gronwall’s inequality, which prevents the need for compactness of the resolvent operator and the standard fixed point theorems. Then, we extend the discussions to the fractional Sobolev-type semilinear integrodifferential systems. Finally, some theoretical and practical examples are provided to illustrate the obtained theoretical results.https://www.mdpi.com/2504-3110/6/2/73fractional integrodifferential systemapproximate controllabilitySchauder’s fixed point theoremresolvent operatorsSobolev-type system |
| spellingShingle | Velusamy Vijayakumar Kottakkaran Sooppy Nisar Dimplekumar Chalishajar Anurag Shukla Muslim Malik Ateq Alsaadi Saud Fahad Aldosary A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators Fractal and Fractional fractional integrodifferential system approximate controllability Schauder’s fixed point theorem resolvent operators Sobolev-type system |
| title | A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators |
| title_full | A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators |
| title_fullStr | A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators |
| title_full_unstemmed | A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators |
| title_short | A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators |
| title_sort | note on approximate controllability of fractional semilinear integrodifferential control systems via resolvent operators |
| topic | fractional integrodifferential system approximate controllability Schauder’s fixed point theorem resolvent operators Sobolev-type system |
| url | https://www.mdpi.com/2504-3110/6/2/73 |
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