The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm

Abstract

The article is devoted to the existence and Hyers-Ulam stability of the almost periodic solution to the fractional differential equation with impulse and fractional Brownian motion under nonlocal condition. The investigation is mainly based on the semigroups of operators method and Mönch fixed points method, as well as the basic theory of Hyers-Ulam stability.

KEYWORDS:

• Impulse fractional stochastic differential equation
• Mönch fixed point theorem
• Hausdorff measure of noncompactness
• Hyers-Ulam stability
• Fractional Brownian motion

2010 MSC:

• 34A08
• 60G22
• 65C30

Additional information

Funding

This work is supported by the Hunan Provincial Natural Science Foundation of China (No. 14JJ2050).