Controllability of Nonlinear Fractional Delay Dynamical Systems. Issue 1 (February 2016)

• Record Type: Journal Article
• Authors: Nirmala, R. Joice; Balachandran, K.; Rodríguez-Germa, L.; Trujillo, J.J.
• Is Part Of: Reports on mathematical physics. Volume 77:Issue 1(2016)
• Page Start: 87
• Page End: 104
• Publication Date: 2016-02
• Subjects: fractional delay differential equation -- Laplace transform -- controllability -- Mittag—Leffler function -- Caputo fractional derivative; 93B05 -- 34A08; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(16)30007-6
• Languages: English
• ISSNs: 0034-4877

Abstract

Abstract : This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag—Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.