Asymptotic Behavior of Neutral Stochastic Partial Functional Integro--Differential Equations Driven by a Fractional Brownian Motion


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.


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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


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