An Analysis on the Optimal Control for Fractional Stochastic Delay Integrodifferential Systems of Order 1 < γ < 2

被引：13

作者：

Johnson, Murugesan ^{[1
]}

Vijayakumar, Velusamy ^{[1
]}

机构：

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

来源：

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

关键词：

stochastic differential equation; optimal controls; integrodifferential systems; fractional calculus; fixed point theorem; APPROXIMATE CONTROLLABILITY; INCLUSIONS; EQUATIONS;

D O I：

10.3390/fractalfract7040284

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to investigate the optimal control for fractional stochastic integrodifferential systems of order 1 < gamma < 2. To ensure the existence and uniqueness of mild solutions, we first gather a novel list of requirements. Further, the existence of optimal control for the stated issue is given by applying Balder's theorem. Additionally, we extend our existence outcomes with infinite delay. The outcomes are obtained via fractional calculus, Holder's inequality, the cosine family, stochastic analysis techniques, and the fixed point approach. The theory is shown by an illustration, as well.

引用

页数：24

共 47 条

[1] A general formulation and solution scheme for fractional optimal control problems [J].

Agrawal, OP .

NONLINEAR DYNAMICS, 2004, 38 (1-4) :323-337

[2]

Arendt W, 2011, MG MATH, V96, pIX, DOI 10.1007/978-3-0348-0087-7

[3] Approximate controllability of second order semilinear stochastic system with nonlocal conditions [J].

Arora, Urvashi ;

Sukavanam, N. .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 258 :111-119

[4] The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators [J].

Balasubramaniam, P. ;

Tamilalagan, P. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2017, 174 (01) :139-155

[5] Approximate Controllability of Second-Order Stochastic Distributed Implicit Functional Differential Systems with Infinite Delay [J].

Balasubramaniam, P. ;

Muthukumar, P. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 143 (02) :225-244

[6] NECESSARY AND SUFFICIENT CONDITIONS FOR L1-STRONG WEAK LOWER SEMICONTINUITY OF INTEGRAL FUNCTIONALS [J].

BALDER, EJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (12) :1399-1404

[7] Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators [J].

Chang, Yong-Kui ;

Pei, Yatian ;

Ponce, Rodrigo .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2019, 182 (02) :558-572

[8] Solvability and optimal controls of non-instantaneous impulsive stochastic fractional differential equation of order q ∈ (1,2) [J].

Dhayal, Rajesh ;

Malik, Muslim ;

Abbas, Syed .

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2021, 93 (05) :780-802

[9] Optimal control problem for some integrodifferential equations in Banach spaces [J].

Diallo, Mouhamadou Alpha ;

Ezzinbi, Khalil ;

Sene, Abdoulaye .

OPTIMAL CONTROL APPLICATIONS & METHODS, 2018, 39 (02) :563-574

[10] A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1 < r < 2 [J].

Dineshkumar, C. ;

Udhayakumar, R. ;

Vijayakumar, V. ;

Nisar, Kottakkaran Sooppy ;

Shukla, Anurag .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2021, 190 :1003-1026

← 1 2 3 4 5 →

An Analysis on the Optimal Control for Fractional Stochastic Delay Integrodifferential Systems of Order 1 &lt; γ &lt; 2

An Analysis on the Optimal Control for Fractional Stochastic Delay Integrodifferential Systems of Order 1 < γ < 2