Brownian motion

Stability (learning theory)

Physics

Mathematics

Stochastic differential equation

Fractional Brownian motion

Statistics

Machine learning

Fractional calculus

Mathematical analysis

Computer science

Quantum mechanics

Differential equation

Applied mathematics

Impulse (physics)

Stochastic Analysis and Applications

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.

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