Abstract
In this study, we are currently investigating the controllability of nonlinear fractional differential control systems with delays in the state function. The solution representations of fractional delay differential equations have been established by using the delayed Mittag-Leffler function. Firstly we obtain the result of the controllability of a linear fractional control system with delay. Then, for the controllability criteria of nonlinear fractional delay system, we establish the set of sufficient conditions of nonlinear fractional differential systems with delay in their state function by using Schauder’s fixed point theorem. In the end, a numerical example is constructed to support the results.
Highlights
The fractional calculus and its applications have become popular because of the differintegral
Approximate controllability results for the nonlinear fractional differential system were discussed by Sakthivel et al in [23, 24]
The previous studies mainly focused on controllability of nonlinear different types of fractional differential systems, but no work has reported on the controllability of nonlinear fractional differential system that discusses pure delay, which is presented in this manuscript
Summary
The fractional calculus and its applications have become popular because of the differintegral. Sakthivel et al [18] established the controllability conditions about nonlinear neutral fractional control systems. Approximate controllability results for the nonlinear fractional differential system were discussed by Sakthivel et al in [23, 24].
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