Archives

Impulsive fractional stochastic differential inclusions driven by sub-Fractional Brownian motion with infinite delay and sectorial operators
by Meryem Chaouche   Toufik Guendouzi

Vol. 16 No. 2 (2021) P.87~P.126
 DOI: https://doi.org/10.21915/BIMAS.2021201 10.21915/BIMAS.2021201

ABSTRACT

We investigate the existence of mild solutions of impulsive fractional stochastic differential inclusions driven by sub-fractional Brownian motion $S_{Q}^{H}$ with infinite delay and non instantaneous impulses when the linear part is a fractional sectorial operators on separable Hilbert spaces. We consider the cases when the multivalued map is convex as well as non convex, a sufficient conditions for the existence are derived with the help of the multivalued fixed point theory and the measure of noncompactness.

KEYWORDS
Mild solution, impulsive fractional stochastic differential inclusions, fractional Brownian motion, fractional sectorial operators, infinite delay, fractional derivative, fixed point.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 26A33, 34A37, 34A60, 34K40, 35R11, 60H15.

MILESTONES