Existence and optimal control results for Caputo fractional delay Clark's subdifferential inclusions of order r∈(1,2) with sectorial operators

Marimuthu Mohan Raja, Velusamy Vijayakumar, Kalyana Chakravarthy Veluvolu, Anurag Shukla, Kottakkaran Sooppy Nisar
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Abstract

In this study, we investigate the effect of Clarke's subdifferential type on the optimal control results for fractional differential systems of order 1<r<2$$ 1<r<2 $$ with delay. The main findings of this study are tested by using multivalued functions, sectorial operators, fractional derivatives, and the fixed point theorem. To begin, the existence of mild solutions is established and verified primarily by using a very well multivalued fixed point theorem and the characteristics of generalized Clarke subdifferential problems. Furthermore, we get a finding on the existence of optimal control for the presented control system under particular reasonable conditions. After that, we will move on to the time optimal control results for the given system. Finally, an example for drawing the theory behind the main conclusions is shown.

Abstract Image

带扇形算子的卡普托分数延迟克拉克子微分方程r∈(1,2)阶存在性和最优控制结果
在本研究中,我们探讨了克拉克子微分类型对有延迟的 1<r<2$$ 1<r<2$$ 阶分数微分系统最优控制结果的影响。利用多值函数、扇形算子、分数导数和定点定理检验了本研究的主要结论。首先,主要通过使用一个非常好的多值定点定理和广义克拉克子微分问题的特征,确定并验证了温和解的存在性。此外,我们还发现了所提出的控制系统在特定合理条件下的最优控制存在性。之后,我们将继续讨论给定系统的时间最优控制结果。最后,我们将举例说明主要结论背后的理论。
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