Asymptotic Behavior of Neutral Stochastic Partial Functional Integro--Differential Equations Driven by a Fractional Brownian Motion
Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 6, p. 407-421.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.007.06.04
Classification : 60H15, 60G15, 60J65
Keywords: Resolvent operators, \(C_0\)-semigroup, Wiener process, Mild solutions, Fractional Brownian motion, Exponential decay of solutions.

Caraballo, Tomás 1 ; Diop, Mamadou Abdoul 2 ; Ndiaye, Abdoul Aziz 3

1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla. Apdo. de Correos, 1160, 41080-Sevilla, Spain
2 Département de Mathématiques, Université Gaston Berger de Saint-Louis, , UFR SAT, 234, Saint-Louis, Sénégal
3 Département de Mathématiques, Université Gaston Berger de Saint-Louis, UFR SAT 234, Saint-Louis, Sénégal
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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 its applications, Tome 7 (2014) no. 6, p. 407-421. doi : 10.22436/jnsa.007.06.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.06.04/

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