Asymptotic Attractivity and Stability for Random Functional Differential Equation

Abstract

The random differential equations appears quite naturally in the study of changes or the rate of change of any processes like diffusion process or Brownian motion. The random differential equations have been the subject of rather extensive research area since long time. It have been utilized as models for a wide variety of random problems that have been encountered time and in the areas of all areas like Sciences and Environmental Sciences. In this paper, we have discussed an existence results for local asymptotic attractivity and asymptotic stability of random solution for nonlinear random functional differential equations in Banach algebra through hybrid random fixed point theorem. The results obtained, is generalize and extend the asymptotic attractivity and stability of random solutions for concerning random functional differential equations.