Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 585--604 | DOI:10.5890/DNC.2020.09.002

Mahamat Hassan Mahamat Hamit$^{1}$, Fulbert Kuessi Allognissode$^{2}$, Mohamed salem Mohamed$^{1}$, Louk-Man Issaka$^{1}$, Mamadou Abdoul Diop$^{1}$,$^{3}$

$^{1}$ Département de Mathématiques, Université Gaston Berger de Saint-Louis, UFR SAT, B.P234, Saint-Louis, Sénégal

$^{2}$ Institut de Mathématiques et de Sciences Physiques, URMPM B.P 613, Porto-Novo, Bénin

$^{3}$ UMMISCO UMI 209 IRD/UPMC, Bondy, France

Abstract

In this work, we consider a class of neutral stochastic integro-differential 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 integro-differential 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 p-stability of the mild solution of the considered equations. An example is presented to demonstrate the obtained theory.

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