Stability result of higher-order fractional neutral stochastic differential system with infinite delay driven by Poisson jumps and Rosenblatt process

Abstract

In this manuscript, we establish the stability results of higher-order fractional neutral stochastic differential system (FNSDs) with infinite delay driven by Poisson jumps and Rosenblatt process via the Nussbaum fixed point theorem. The results are obtained by a new integral inequality. The validation of the efficiency of the proposed method is done through a numerical example.

Keywords:

• Fractional calculus
• Mild solution
• Second order stochastic differential system
• Exponential stability
• Rosenblatt process
• Poisson jumps

MATHEMATICS SUBJECT CLASSIFICATION:

• 26A33
• 34A08
• 45M10
• 34A12
• 35J05
• 60H20