Affiliation:
1. School of Basic Sciences, Indian Institute of Technology , Mandi , Himachal Pradesh , India
Abstract
Abstract
In this manuscript, we investigate the existence, uniqueness, Hyer-Ulam stability and controllability analysis for a fractional dynamic system on time scales. Mainly, this manuscript has three segments: In the first segment, we give the existence of solutions. The second segment is devoted to the study of stability analysis while in the last segment, we establish the controllability results. We use the Banach and nonlinear alternative Lery-Schauder–type fixed point theorem to establish these results. Also, we give some numerical examples for different time scales. Moreover, we give two applications to outline the effectiveness of these obtained results.
Funder
University Grants Commission
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Reference49 articles.
1. R. L. Magin, Fractional Calculus in Bioengineering, vol. 2, Connecticut, Begell House, 2006, 6.
2. H. Rudolf, Ed. in Applications of Fractional Calculus in Physics, vol. 128, Singapore, World Scientific, 2000.
3. R. L. Bagley and P. J. Torvik, “A theoretical basis for the application of fractional calculus to viscoelasticity,” J. Rheol., vol. 27, no. 3, pp. 201–210, 1983, https://doi.org/10.1122/1.549724.
4. V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, HEP, Springer, 2011.
5. H. A. A. El-Saka, A. A. M. Arafa, and M. I. Gouda, “Dynamical analysis of a fractional SIRS model on homogenous networks,” Adv. Differ. Equ., vol. 2019, no. 1, p. 144, 2019, https://doi.org/10.1186/s13662-019-2079-3.
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