Asymptotic Behavior of Neutral Stochastic Partial Functional Integro--Differential Equations Driven by a Fractional Brownian Motion
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Authors
Tomás Caraballo
- Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla. Apdo. de Correos, 1160, 41080-Sevilla, Spain.
Mamadou Abdoul Diop
- Département de Mathématiques, Université Gaston Berger de Saint-Louis, , UFR SAT, 234, Saint-Louis, Sénégal.
Abdoul Aziz Ndiaye
- Département de Mathématiques, Université Gaston Berger de Saint-Louis, UFR SAT 234, Saint-Louis, Sénégal.
Abstract
This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic
delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst
parameter \(H \in ( \frac{1}{2} , 1)\). The main tools for the existence of solution is a fixed point theorem and the theory of
resolvent operators developed in Grimmer [R. Grimmer, Trans. Amer. Math. Soc., 273 (1982), 333-349.],
while a Gronwall-type lemma plays the key role for the asymptotic behavior. An example is provided to
illustrate the results of this work.
Share and Cite
ISRP Style
Tomás Caraballo, Mamadou Abdoul Diop, Abdoul Aziz Ndiaye, Asymptotic Behavior of Neutral Stochastic Partial Functional Integro--Differential Equations Driven by a Fractional Brownian Motion, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 6, 407--421
AMA Style
Caraballo Tomás, Diop Mamadou Abdoul, Ndiaye Abdoul Aziz, Asymptotic Behavior of Neutral Stochastic Partial Functional Integro--Differential Equations Driven by a Fractional Brownian Motion. J. Nonlinear Sci. Appl. (2014); 7(6):407--421
Chicago/Turabian Style
Caraballo, Tomás, Diop, Mamadou Abdoul, Ndiaye, Abdoul Aziz. "Asymptotic Behavior of Neutral Stochastic Partial Functional Integro--Differential Equations Driven by a Fractional Brownian Motion." Journal of Nonlinear Sciences and Applications, 7, no. 6 (2014): 407--421
Keywords
- Resolvent operators
- \(C_0\)-semigroup
- Wiener process
- Mild solutions
- Fractional Brownian motion
- Exponential decay of solutions.
MSC
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