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

被引：5

作者：

Sivasankar, Sivajiganesan ^{[1
]}

Udhayakumar, Ramalingam ^{[1
]}

Muthukumaran, Venkatesan ^{[2
]}

Madhrubootham, Saradha ^{[3
]}

AlNemer, Ghada ^{[4
]}

Elshenhab, Ahmed M. ^{[5
,6
]}

机构：

[1] Vellore Inst Technol, Sch Adv Sci, Dept Math, Vellore 632014, Tamil Nadu, India

[2] SRM Inst Sci & Technol, Coll Engn & Technol, Dept Math, Kattankulathur 603203, Tamilnadu, India

[3] REVA Univ, Sch Appl Sci, Dept Math, Bangalore 560064, Karnataka, India

[4] Princess Nourah bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia

[5] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China

[6] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

来源：

FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 04期

关键词：

Hilfer fractional derivative (HFD); stochastic evolution Equation (SEE); Sobolev-type system; neutral system; optimal controls (OC); hemivariational inequalities; nonlocal condition; APPROXIMATE CONTROLLABILITY; EQUATIONS; SOLVABILITY; INCLUSIONS;

D O I：

10.3390/fractalfract7040303

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：22

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