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

Author:

Mohan Raja Marimuthu1ORCID,Vijayakumar Velusamy2ORCID,Veluvolu Kalyana Chakravarthy1ORCID,Shukla Anurag3ORCID,Nisar Kottakkaran Sooppy4ORCID

Affiliation:

1. School of Electronics Engineering Kyungpook National University Daegu South Korea

2. Department of Mathematics, School of Advanced Sciences Vellore Institute of Technology Vellore Tamil Nadu India

3. Department of Applied Science Rajkiya Engineering College Kannauj Kannauj India

4. Department of Mathematics, College of Science and Humanities in Alkharj Prince Sattam Bin Abdulaziz University Alkharj Saudi Arabia

Abstract

AbstractIn this study, we investigate the effect of Clarke's subdifferential type on the optimal control results for fractional differential systems of order 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.

Publisher

Wiley

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