Abstract
This paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion , with Hurst parameter . 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.
Funding statement: The authors are supported by CEA-MITIC (Gaston Berger University (UGB), UFR Sciences Appliquées et de Technologie, Saint-Louis, Sénégal, CEA-SMA (Université d’Abomey-Calavi (UAC), Institut de Mathématiques et de Sciences Physiques, Porto Novo, Benin) and Réseau EDP Modélisation et Contrôle.
Acknowledgements
The authors are very much thankful to the editor and the referees for the interesting remarks and comments which helped to improve the paper.
References
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