Abstract
In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
Reference39 articles.
1. "[1] A.A. Kilbas, H.M. Srivastava, and J.J. Trujilo, Theory and applications of fractional differential equations, North Holland Mathematics Studies, vol.204, Elsevier Science BV, Amsterdam, 2006.
2. [2] A.A. Tolstonogov, Differential Inclusion in a Banach Space,} Kluwer Academic, Dordrecht, 2000.
3. [3] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.
4. [4] C. Tudor, Some properties of the sub-fractional Brownian motion, Stochastics: An Intenational Jourmal of Probability and Stochastic Processes 79 (2007), 431-448. https://doi.org/10.1080/17442500601100331
5. [5] D. Nualart, The Malliavin Calculus and related Topics, 2nd edn. Springer, Berlin, 2006.