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<p>This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces. Moreover, we establish the controllability of the considered system. To do so, first, we investigate the approximate controllability of the corresponding linear system. Subsequently, we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable. To reach the conclusions, the theory of resolvent operators, the Banach contraction mapping principle, and fixed point theorems are used. While concluding, some examples are given to demonstrate the efficacy of the proposed results.</p>

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Approximate controllability of nonlinear evolution fractional control system with delay

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Kamla Kant Mishra,
  • Shruti Dubey

摘要

This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces. Moreover, we establish the controllability of the considered system. To do so, first, we investigate the approximate controllability of the corresponding linear system. Subsequently, we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable. To reach the conclusions, the theory of resolvent operators, the Banach contraction mapping principle, and fixed point theorems are used. While concluding, some examples are given to demonstrate the efficacy of the proposed results.