Non-instantaneous impulsive Hilfer–Katugampola fractional stochastic differential equations with fractional Brownian motion and Poisson jumps

Abstract

The existence of solutions of non-instantaneous impulsive Hilfer–Katugampola fractional differential equations of order 1 / 2 < α < 1 and parameter 0 ≤ β ≤ 1 with fractional Brownian motion (fBm) and Poisson jumps is investigated in this paper. The required results are obtained based on fractional calculus, stochastic analysis, semigroups, and the fixed point theorem. In the end of the paper, an example is provided to illustrate the applicability of the theoretical results.