Discontinuity, Nonlinearity, and Complexity
Attractiveness and Exponential pStability of Neutral Stochastic Functional Integrodifferential Equations Driven by Wiener Process and fBm with Impulses Effects
Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 585604  DOI:10.5890/DNC.2020.09.002
Mahamat Hassan Mahamat Hamit$^{1}$, Fulbert Kuessi Allognissode$^{2}$, Mohamed salem Mohamed$^{1}$, LoukMan Issaka$^{1}$, Mamadou Abdoul Diop$^{1}$,$^{3}$
$^{1}$ Département de Mathématiques, Université Gaston Berger de SaintLouis, UFR SAT, B.P234, SaintLouis, Sénégal
$^{2}$ Institut de Mathématiques et de Sciences Physiques, URMPM B.P 613, PortoNovo, Bénin
$^{3}$ UMMISCO UMI 209 IRD/UPMC, Bondy, France
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Abstract
In this work, we consider a class of neutral stochastic integrodifferential equations driven by Wiener process and fractional Brownian motion with impulses effects. This paper deals with the global attractiveness and quasiinvariant sets for neutral stochastic integrodifferential equations driven by Wiener process and fractional Brownian motion with impulses effects in Hilbert spaces. We use new integral inequalities combined with theoriesof resolvent operators to establish a set of sufficient conditions for the exponential pstability of the mild solution of the considered equations. An example is presented to demonstrate the obtained theory.
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