Existence of Sobolev-Type Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities and Optimal Controls-Reference-Cited by-同舟云学术

Existence of Sobolev-Type Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities and Optimal Controls

Published:2023-03-30 Issue:4 Volume:7 Page:303
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Sivasankar Sivajiganesan¹^ORCID,Udhayakumar Ramalingam¹^ORCID,Muthukumaran Venkatesan²^ORCID,Madhrubootham Saradha³,AlNemer Ghada⁴^ORCID,Elshenhab Ahmed M.⁵⁶^ORCID

Affiliation:

1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India

2. Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India

3. Department of Mathematics, School of Applied Sciences, REVA University, Bangalore 560064, Karnataka, India

4. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

5. School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

6. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Abstract

This article concentrates on a control system with a nonlocal condition that is driven by neutral stochastic evolution hemivariational inequalities (HVIs) of Sobolev-type Hilfer fractional (HF). In order to illustrate the necessary requirements for the existence of mild solutions to the required control system, we first use the characteristics of the modified Clarke sub-differential and a fixed point approach for multivalued functions. Then, we show that there are optimal state-control sets that are driven by Sobolev-type HF neutral stochastic evolution HVIs utilizing constrained Lagrange optimal systems. The optimal control (OC) results are created without taking the uniqueness of the control system solutions into account. Finally, the main finding is shown by an example.

Funder

Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/4/303/pdf

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3. Quasi-static hemivariational inequality via vanishing acceleration approach;Ochal;SIAM J. Math. Anal.,2009