The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators

Balasubramaniam, P.; Tamilalagan, P.

doi:10.1007/s10957-016-0865-6

Cited by 65 publications

(37 citation statements)

References 31 publications

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“…On the other hand, controllability for various linear and nonlinear dynamical systems have been considered in many publications by using different approaches due to its applications in many fields of science and engineering, see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. It should be emphasized that there are many different notions of controllability for dynamical systems, for example, approximate controllability, exact controllability, null controllability, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…For details, see [33][34][35][36][37][38][39] and the references therein. In particular, some researchers investigated controllability of stochastic dynamical control systems in infinite-dimensional spaces, see [26][27][28][29][30][31]. However, there are few works that have reported about the study of controllability problems for stochastic evolution equations with nonlocal conditions, see [30,31], and the authors suppose that the nonlocal item g is a completely continuous map in these papers.…”

Section: Introductionmentioning

confidence: 99%

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Finite-approximate controllability of fractional stochastic evolution equations with nonlocal conditions

Ding

2020

J Inequal Appl

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This paper deals with the finite-approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We establish sufficient conditions for the finite-approximate controllability of the control system when the compactness conditions or Lipschitz conditions for the nonlocal term and uniform boundedness conditions for the nonlinear term are not required. The discussion is based on the fixed point theorem, approximation techniques and diagonal argument. In the end, an example is presented to illustrate the abstract theory. Our result improves and extends some relevant results in this area.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite-approximate controllability of fractional stochastic evolution equations with nonlocal conditions

Ding

2020

J Inequal Appl

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“…24,25 Motivated by the above consideration, in this paper, we will study the Lagrange problem of systems governed by impulsive partial stochastic differential equations and an existence result of optimal controls is presented. The known results appeared in other works [22][23][24][25] are generalized to the impulsive stochastic control systems with weighted pseudo almost periodic coefficients settings.…”

Section: Introductionmentioning

confidence: 99%

A class of stochastic hyperbolic evolution equations via weighted pseudo almost periodic coefficients and optimal controls

Zhang

Han

2019

Optim Control Appl Methods

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Summary This paper introduces the concept of the piecewise weighted pseudo periodicity for stochastic processes. In addition, it establishes a new composition theorem for weighted pseudo almost periodic functions under the non‐Lipschitz conditions. Using this composition theorem, evolution family together with a fixed‐point theorem for condensing maps, we investigate the existence of p‐mean piecewise weighted pseudo almost periodic mild solutions and optimal mild solutions for a class of impulsive stochastic hyperbolic evolution equations in Hilbert spaces. Then, the existence conditions of optimal pairs of systems governed by the nonlinear impulsive stochastic evolution equations are presented. Finally, an example is provided to illustrate the obtained theory.

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“…Using the LeraySchauder fixed point theorem, Balasubramaniam and Tamilalagan [2] studied the solvability and optimal controls for impulsive fractional stochastic integro-differential equations. Recently, Tamilalagan and Balasubramaniam [18] investigated the solvability and optimal controls for fractional stochastic differential equations driven by Poisson jumps in Hilbert space by using analytic resolvent operators and classical Banach contraction mapping principle.…”

Section: Introductionmentioning

confidence: 99%

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

Kumar

2017

Cubo

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This paper deals with fractional optimal control for a class of semilinear stochastic equation in Hilbert space setting. To ensure the existence and uniqueness of mild solution, a set of sufficient conditions is constructed. The existence of fractional optimal control for semilinear stochastic system is also discussed. Finally, an example is included to show the applications of the developed theory. RESUMENEste artículo estudia el controlóptimo fraccional para una clase de ecuaciones estocásticas semilineales en un contexto de espacios de Hilbert. Para asegurar la existencia y la unicidad de soluciones blandas, construimos un conjunto de condiciones suficientes. La existencia del controlóptimo fraccional para sistemas estocásticos semilineales también es discutido. Finalmente, incluimos un ejemplo para mostrar la aplicabilidad de la teoría desarrollada.

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The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators

Cited by 65 publications

References 31 publications

Finite-approximate controllability of fractional stochastic evolution equations with nonlocal conditions

Finite-approximate controllability of fractional stochastic evolution equations with nonlocal conditions

A class of stochastic hyperbolic evolution equations via weighted pseudo almost periodic coefficients and optimal controls

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

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