Displaying similar documents to “Existence and controllability of fractional-order impulsive stochastic system with infinite delay”

Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps

Chinnathambi Rajivganthi, Krishnan Thiagu, Palanisamy Muthukumar, Pagavathigounder Balasubramaniam (2015)

Applications of Mathematics

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The paper is motivated by the study of interesting models from economics and the natural sciences where the underlying randomness contains jumps. Stochastic differential equations with Poisson jumps have become very popular in modeling the phenomena arising in the field of financial mathematics, where the jump processes are widely used to describe the asset and commodity price dynamics. This paper addresses the issue of approximate controllability of impulsive fractional stochastic differential...

Controllability criteria for time-delay fractional systems with a retarded state

Beata Sikora (2016)

International Journal of Applied Mathematics and Computer Science

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The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient...

Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Rajagopal Joice Nirmala, Krishnan Balachandran (2017)

Kybernetika

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This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Shanmugasundaram Karthikeyan, Krishnan Balachandran, Murugesan Sathya (2015)

International Journal of Applied Mathematics and Computer Science

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This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability...

Controllability of nonlinear impulsive Ito type stochastic systems

Rathinasamy Sakthivel (2009)

International Journal of Applied Mathematics and Computer Science

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In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.

Controllability of nonlinear implicit fractional integrodifferential systems

Krishnan Balachandran, Shanmugam Divya (2014)

International Journal of Applied Mathematics and Computer Science

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In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.

Stochastic controllability of linear systems with state delays

Jerzy Klamka (2007)

International Journal of Applied Mathematics and Computer Science

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A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability...

Schauder's fixed-point theorem in approximate controllability problems

Artur Babiarz, Jerzy Klamka, Michał Niezabitowski (2016)

International Journal of Applied Mathematics and Computer Science

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The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder's fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions,...

Cone-type constrained relative controllability of semilinear fractional systems with delays

Beata Sikora, Jerzy Klamka (2017)

Kybernetika

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The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function f . The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are...

Stochastic controllability of systems with multiple delays in control

Jerzy Klamka (2009)

International Journal of Applied Mathematics and Computer Science

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Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved...

Constrained controllability of nonlinear stochastic impulsive systems

Shanmugasundaram Karthikeyan, Krishnan Balachandran (2011)

International Journal of Applied Mathematics and Computer Science

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This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.