Controllability of damped dynamical systems modelled by Hilfer fractional derivatives. Issue 1 (31st December 2022)

• Record Type: Journal Article
• Authors: Naveen, S.; Srilekha, R.; Suganya, S.; Parthiban, V.
• Is Part Of: Journal of Taibah University for science. Volume 16:Issue 1(2022)
• Page Start: 1254
• Page End: 1263
• Publication Date: 2022-12-31
• Subjects: Gramian matrix -- Laplace transform -- Mittag-Leffler function -- numerical technique -- successive approximation technique; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2022.2157188
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract : In this article, we investigate the controllability of damped dynamical system modelled by Hilfer derivative of fractional order τ 1 ∈ ( 1, 2 ] and τ 2 ∈ ( 0, 1 ] . The Mittag-Leffler matrix function of two parameters has been used to represent the solution of Hilfer fractional problem of damped dynamical system. With the use of the Schawder fixed point theorem and the contraction mapping theorem, the existence and uniqueness of the linear and non-linear system of Hilfer dynamical control system are determined. More specifically, fractional calculus are used to provide sufficient criteria for the controllability results. Finally, examples are given to show how the key results might be justified.