Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay

Bahuguna, D.; Sakthivel, R.; Chadha, Alka

doi:10.1080/07362994.2016.1249285

Cited by 27 publications

(8 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the past decades, the theory of impulsive differential equations has become an active area due to its wide applications in several fields such as communications, mechanics, electrical engineering, medicine, biology, etc. For the basic theory of impulsive differential equations, we refer the readers to [2,4,5,6,10,21,27,33] and the references therein.…”

Section: (Communicated By Peter E Kloeden)mentioning

confidence: 99%

Long time behavior of fractional impulsive stochastic differential equations with infinite delay

Xu¹,

Caraballo²

2019

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive stochastic differential equations with infinite delay driven by both K-valued Q-cylindrical Brownian motion and fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). A general framework which provides an effective way to prove the continuous dependence of mild solutions on initial value is established under some appropriate assumptions. Furthermore, it is also proved the exponential decay to zero of solutions to fractional stochastic impulsive differential equations with infinite delay.

show abstract

Section: (Communicated By Peter E Kloeden)mentioning

confidence: 99%

Long time behavior of fractional impulsive stochastic differential equations with infinite delay

Xu¹,

Caraballo²

2019

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

show abstract

“…The interest in describing such processes by appropriated mathematical models, which are so-called differential equations with impulsive effects, mainly arose in recent years. In the simulations of such systems it is often convenient to neglect the durations of the rapid changes and to assume that the changes are represented by state jumps, see, e.g., [2,7,9,13].…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay

Zhang

Caraballo

2019

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

This paper is concerned with the well-posedness and dynamics of (delete) a delay impulsive fractional stochastic evolution equations with time fractional differential operator α ∈ (0, 1). After establishing the well-posedness of the problem, and a result ensuring the existence and uniqueness of mild solutions globally defined in future, the existence of a minimal global attracting set is investigated in the mean-square topology, under general assumptions not ensuing the uniqueness of solutions. Furthermore, in the case of uniqueness, it is possible to provide more information about the geometrical structure of such global attracting set. In particular, it is proved that the minimal compact globally attracting set for the solutions of the problem becomes a singleton. It is remarkable that the attraction property is proved in the usual forward sense, unlike the pullback concept used in the context of random dynamical systems, but the main point is that the model under study has not been proved to generate a random dynamical system.

show abstract

“…Liu and Wang [5] considered the solvability and optimal controls for systems governed by semi-linear impulsive fractional differential equations of order ]0, 1]. Since noise or stochastic perturbation are unavoidable in real world [6,7], it is of interest to consider stochastic effects in optimal control problems. Balasubramaniam and Tamilalagan [8] investigated the solvability and optimal controls for fractional stochastic systems of order in ]0, 1].…”

Section: Introductionmentioning

confidence: 99%

Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators

Chang

Pei

Ponce

2018

J Optim Theory Appl

View full text Add to dashboard Cite

This paper is mainly concerned with controlled stochastic evolution equations of Sobolev type for the Caputo and Riemann-Liouville fractional derivatives. Some sufficient conditions are established for the existence of mild solutions and optimal state-control pairs of the limited Lagrange optimal systems. The main results are investigated by compactness of fractional resolvent operator family, and the optimal control results are derived without uniqueness of solutions for controlled evolution equations.

show abstract

Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay

Cited by 27 publications

References 32 publications

Long time behavior of fractional impulsive stochastic differential equations with infinite delay

Long time behavior of fractional impulsive stochastic differential equations with infinite delay

Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay

Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators

Contact Info

Product

Resources

About