Abstract
We discuss the controllability for a damped fractional differential system with impulses and state delay, which involves Caputo fractional derivatives. Deriving the condition based on the Gramian matrix defined by the Mittag-Leffler matrix function and Laplace transformation, we establish necessary and sufficient conditions of controllability criteria. Finally, we construct two numerical examples to support the result.
Highlights
The fractional differential equations have proven to be a useful tool for modeling distinct phenomena in various fields of physics, engineering, and economics
In recent years, controllability problems for linear and nonlinear fractional differential system are discussed by Matar and Nawaz [32,33,34,35], and partial controllability of various semilinear systems is discussed in [36,37,38,39,40,41,42,43,44,45]
Still no work is reported on the controllability of the damped fractional differential system with impulses and state delay
Summary
The fractional differential equations have proven to be a useful tool for modeling distinct phenomena in various fields of physics, engineering, and economics. The controllability criteria for linear and nonlinear fractional differential systems with state delay and impulses is studied in [62, 63]. The study of the damped fractional differential system for its controllability results by using the Mittag-Leffler matrix function and Gramian matrix is presented in [68].
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