Sobolev-type nonlinear Hilfer fractional stochastic differential equations with noninstantaneous impulsive

Abstract

The existence of a mild solution for nonlinear Hilfer fractional stochastic differential equations of the Sobolev type with non-instantaneous impulse in Hilbert space is investigated in this study. For nonlinear Hilfer fractional stochastic differential equations of Sobolev type with non-instantaneous impulsive conditions, sufficient criteria for controllability are established. Finally, an illustration of the acquired results is shown.

Keywords

• sobolev-type nonlinear hilfer fractional stochastic differential equation
• existence solutions
• controllability
• noninstantaneous impulsive condition