A Grammian matrix and controllability study of fractional delay integro-differential Langevin systems

Hasanen A. Hammad; Mohammed E. Dafaalla; Kottakkaran Sooppy Nisar; Hasanen A. Hammad; Mohammed E. Dafaalla; Kottakkaran Sooppy Nisar

doi:10.3934/math.2024748

AIMS Mathematics

2024, Volume 9, Issue 6: 15469-15485. doi: 10.3934/math.2024748

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A Grammian matrix and controllability study of fractional delay integro-differential Langevin systems

1.
Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
2.
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, India
3.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
4.
Department of Mathematics, College of Science, University of Kordofan, Sudan
5.
Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, 11942, Saudi Arabia

Received: 17 February 2024 Revised: 13 April 2024 Accepted: 19 April 2024 Published: 28 April 2024
MSC : 26A33, 34A08, 34B15, 47H10

This study focused on introducing a fresh model of fractional operators incorporating multiple delays, termed fractional integro-differential Langevin equations with multiple delays. Additionally, the research evaluated the relative controllability of this model within finite-dimensional spaces. Employing fixed-point theory yields the desired outcomes, with the controllability assessment facilitated by Schauder's fixed point and the Grammian matrix defined through the Mittag-Leffler matrix function. Validation of the results was conducted through an application.
- Langevin system,
- integro-differential equation,
- fixed point technique,
- controllability,
- delay term,
- fractional derivatives
Citation: Hasanen A. Hammad, Mohammed E. Dafaalla, Kottakkaran Sooppy Nisar. A Grammian matrix and controllability study of fractional delay integro-differential Langevin systems[J]. AIMS Mathematics, 2024, 9(6): 15469-15485. doi: 10.3934/math.2024748

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Abstract

This study focused on introducing a fresh model of fractional operators incorporating multiple delays, termed fractional integro-differential Langevin equations with multiple delays. Additionally, the research evaluated the relative controllability of this model within finite-dimensional spaces. Employing fixed-point theory yields the desired outcomes, with the controllability assessment facilitated by Schauder's fixed point and the Grammian matrix defined through the Mittag-Leffler matrix function. Validation of the results was conducted through an application.

References

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