On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation

Abstract

In this paper, we studied an averaging principle for Caputo–Hadamard fractional stochastic differential pantograph equation (FSDPEs) driven by Brownian motion. In light of some suggestions, the solutions to FSDPEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. We expand the classical Khasminskii approach to Caputo–Hadamard fractional stochastic equations by analyzing systems solutions before and after applying averaging principle. We provided an applied example that explains the desired results to us.