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Mamadou Abdoul Diop,Khalil Ezzinbi,Modou Lo 대한수학회 2019 대한수학회지 Vol.56 No.1
In this work, we study the existence, uniqueness and stability in the $\alpha$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer \cite{GP} and the nonlinear part satisfies a H\"older type condition with respect to the $\alpha$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment ($p > 2$). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.
STABILITY IN THE α-NORM FOR SOME STOCHASTIC PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS
Diop, Mamadou Abdoul,Ezzinbi, Khalil,Lo, Modou Korean Mathematical Society 2019 대한수학회지 Vol.56 No.1
In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.
Diop, Mamadou Abdoul,Rathinasamy, Sakthivel,Ndiaye, Abdoul Aziz Springer-Verlag 2016 MEDITERRANEAN JOURNAL OF MATHEMATICS Vol.13 No.5
<P>This paper deals with the existence,uniqueness and asymptotic behaviors of mild solutions to neutral stochastic delay functional integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion B (H) , with Hurst parameter . We use the theory of resolvent operators developed in Grimmer (Trans Am Math Soc 273(1982):333-349, 2009) to show the existence of mild solutions. An example is provided to illustrate the results of this work.</P>
K. Ramkumar,K. Ravikumar,Dimplekumar Chalishajar,A. Anguraj,Mamadou Abdoul Diop 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.
K. RAMKUMAR,K. RAVIKUMAR,DIMPLEKUMAR CHALISHAJAR,A. ANGURAJ,MAMADOU ABDOUL DIOP The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.