Browsing by Author "Diop, Mamadou Abdoul"
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Item Allognissode, F.K, Diop, M.A, Ezzinbi, K, Ogouyandjou, C. (2019) Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior, Random Operators and Stochastic Equations. https://doi.org/10.1515/rose-2019-2009(De Gruyter, 2019-05-10) Allognissode, Fulbert Kuessi; Diop, Mamadou Abdoul; Ezzinbi, Khalil; Ogouyandjou, CarlosThis paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion S[H/Q] (t), with Hurst parameter H∈(1\2,1). By the theory of resolvent operator developed by R. Grimmer (1982) to establish the existence of mild solutions, we give sufficient conditions ensuring the existence, uniqueness and the asymptotic behavior of the mild solutions. An example is provided to illustrate the theory.Item Almost sure asymptotic stability for some stochastic partial functional integrodifferential equations on Hilbert spaces(Taylor and Francis Online, 2019-04-25) Dieye, Moustapha; Diop, Mamadou Abdoul; Ezzinbi, KhalilIn this work, we study the asymptotic behavior of the mild solutions of a class of stochastic partial functional integrodifferential equation on Hilbert spaces. Using the stochastic convolution developed, we establish the exponential stability in mean square with p ≥ 2. Also, pathwise exponential stability is proved for p> 2. We extend the result of an example is provided for illustration.Item Asymptotic behavior of a class(Research Gate, 2019-07-13) Bete, Hafiz Kora; Mane, Aziz; Ogouyandjou, Carlos; Diop, Mamadou AbdoulThis paper is devoted to the existence and asymptotic behavior in p-th moment of the mild solution to a class of impulsive neutral stochastic functional integrodifferential equations with infinite delay in Hilbert spaces. A new and sufficient set of conditions are formulated concerning the existence of solutions and the stability of the nonlinear stochastic system. To obtain the desired result, the theory of the resolvent operator in the sense of Grimmer, the stochastic analysis theory, the fixed point theorem and the Hausdorff measure of non-compactness are used. However, it is very important to specify that in this paper, we have left the classical framework in which the nonlinear terms are assumed to be Lipschitz continuous. At the end of this paper, an illustration is also given to show the application of our results.Item Asymptotic behavior of neutral stochastic(Research Gate, 2014-12) Caraballo, Tom´as; Diop, Mamadou Abdoul; Ndiaye, Abdoul AzizThis 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 ∈ (12, 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. (c) 2014 All rights reserved.Item Asymptotic behaviour of mild solution(Vilnius University Press, 2019-06-27) Diop, Mamadou Abdoul; Amoussoub, Amour Toffodji Gbaguidi; Ogouyandjou, Carlos; Sakthivel, RathinasamThis paper presents conditions to assure existence, uniqueness and stability for impulsive neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps. The Banach fixed point theorem and the theory of resolvent operator developed by Grimmer [R.C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc., 273(1):333–349, 1982] are used. An example illustrates the potential benefits of these results.Item Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations driven by Rosenblatt process(Vilnius University Press, 2019-06-27) Diop, Mamadou Abdoul; Amoussou, Amour Toffodji Gbaguidi; Ogouyandjou, Carlos; Sakthivel, RathinasamyThis paper presents conditions to assure existence, uniqueness and stability for impulsive neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps. The Banach fixed point theorem and the theory of resolvent operator developed by Grimmer [R.C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc., 273(1):333–349, 1982] are used. An example illustrates the potential benefits of these results.Item Existence and Uniqueness of Mild Solutions of Stochastic Partial Integro-Differential Impulsive Equations with Infinite Delay via Resolvent Operator(2019) Ravikumar, Kasinathan; Amoussou, Amour T. Gbaguidi; Ogouyandjou, Carlos; Diop, Mamadou AbdoulIn this paper, we investigate the existence of mild solutions for a class of stochastic functional differential impulsive equations with infinite delay on Hilbert space. The results are obtained by using the Banach fixed point theorem and Krasnoselskii–Schaefer type fixed point theorem combined with theories of resolvent operators. In the end as an application, an example has been presented to illustrate the results obtained.Item On the attractivity of an integrodifferential system with state-dependent delay(2019) Bete, Kora Hafiz; Ogouyandjou, Carlos; Diop, Amadou; Diop, Mamadou AbdoulThis work is focused on the existence and attractivity of mild solutions for an integrodifferential system with state dependent delay. The results presented here were established by means of a fixed point theorem due to [T. A. Burton, C. Kirk, Math. Nachr., 189 (1998), 23–31]. At the end, the obtained results are illustrated by an example.