Approximate Controllability of Impulsive Fractional Integro-Differential Systems with Nonlocal Conditions in Hilbert Space

Balasubramaniam, P.; Vembarasan, V.; Senthilkumar, T.

doi:10.1080/01630563.2013.811420

Cited by 55 publications

(21 citation statements)

References 25 publications

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“…The ap-proximate controllability is the weaker concept of controllability receiving much attention. In this case it is possible to steer the system to an arbitrary small neighborhood of the final state [17,18,20,21,24,32,33,35,50,51]. However, stochastic control theory which is a generalization of classical control theory has rarely been reported.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Chadha¹,

Bora²,

Sakthivel³

2018

DSA

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This paper studies the approximate controllability of an impulsive neutral stochastic integro-differential equation with nonlocal conditions and infinite delay involving the Caputo fractional derivative of order q ∈ (1, 2) in separable Hilbert space. The existence of the mild solution to fractional stochastic system with nonlocal and impulsive conditions is first proved utilizing fixed point theorem, stochastic analysis, fractional calculus and solution operator theory. Then, a new set of sufficient conditions proving approximate controllability of nonlocal semilinear fractional stochastic system involving impulsive effects is derived by assuming the associated linear system is approximately controllable. Illustrating the obtained abstract results, an example is considered at the end of the paper.

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Section: Introductionmentioning

confidence: 99%

“…For more details, see [15,19,22,29,39,43,44,45,47,48] and references cited therein. For the study of differential equations with nonlocal initial conditions, we refer to the papers [11,12,17,19,20,36,37,39,40,42,44,49,50,52].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Chadha¹,

Bora²,

Sakthivel³

2018

DSA

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“…Then many important results relative to differential equation (1) with different initial conditions and boundary conditions have been obtained (e.g. [2][3][4][5][6][7][8][9][10][11][12][13][14]). Scholars now find that fractional-order models are more adequate than integer-order models for problems in various fields of science such as physics, fluid flows, electrical networks, and many other (e.g.…”

Section: Introductionmentioning

confidence: 99%

Solutions of fractional differential equations with p-Laplacian operator in Banach spaces

Tan

2018

Bound Value Probl

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In this paper, we study the solutions for nonlinear fractional differential equations with p-Laplacian operator nonlocal boundary value problem in a Banach space. By means of the technique of the properties of the Kuratowski noncompactness measure and the Sadovskii fixed point theorem, we establish some new existence criteria for the boundary value problem. As application, an interesting example is provided to illustrate the main results.

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“…Approximate controllability for semilinear deterministic and stochastic control systems can be found in Mahmudov [26]. Moreover, there are many researchers discussing the approximate controllability for the stochastic fractional systems; for example, see [4,7,33], and the references therein.…”

mentioning

confidence: 99%

“…Slama and Boudaoui [40] obtained sufficient conditions for the existence of mild solutions for the fractional impulsive stochastic differential equation with nonlocal conditions and infinite delay. For more details see [4,33,39] and the references contained therein.…”

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confidence: 99%

Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay

Slama

Boudaoui

2017

Arab. J. Math.

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In this paper we consider a class of fractional nonlinear neutral stochastic evolution inclusions with nonlocal initial conditions in Hilbert space. Using fractional calculus, stochastic analysis theory, operator semigroups and Bohnenblust-Karlin's fixed point theorem, a new set of sufficient conditions are formulated and proved for the existence of solutions and the approximate controllability of fractional nonlinear stochastic differential inclusions under the assumption that the associated linear part of the system is approximately controllable. An example is provided to illustrate the theory. Mathematics Subject Classification

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Approximate Controllability of Impulsive Fractional Integro-Differential Systems with Nonlocal Conditions in Hilbert Space

Cited by 55 publications

References 25 publications

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Solutions of fractional differential equations with p-Laplacian operator in Banach spaces

Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay

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