Controllability of multi-term fractional-order impulsive dynamical systems with $\varphi $-Caputo fractional derivative

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发表日期：

2025年3月24日

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Md. Samshad Hussain Ansari,
Muslim Malik

摘要

In this article, we consider a multi-term $\varphi $ $φ$ -Caputo fractional dynamical system with non-instantaneous impulses. Firstly, we derive the solution for the linear $\varphi $ $φ$ -Caputo fractional differential equation by using the generalized Laplace transform. Then, some necessary and sufficient conditions have been examined for the controllability of the linear multi-term $\varphi $ $φ$ -Caputo fractional dynamical system with non-instantaneous impulses. Further, we establish some sufficient conditions for the controllability of the nonlinear system by utilizing the Schauder’s fixed point theorem and Gramian matrix. Finally, a simulated example is used to validate the obtained results of this article.

Controllability of multi-term fractional-order impulsive dynamical systems with \(\varphi \)-Caputo fractional derivative

摘要