Khasminskii Approach for $$\psi $$-Caputo Fractional Stochastic Pantograph Problem

Abstract

In this manuscript, we study an averaging principle for fractional stochastic pantograph differential equations (FSDPEs) in the $$\psi $$ ψ -sense accompanied by Brownian movement. Under certain assumptions, we are able to approximate solutions for FSPEs by solutions to averaged stochastic systems in the sense of mean square. Analysis of system solutions before and after the average allows extending the classical Khasminskii approach to random fractional differential equations in the sense of $$\psi $$ ψ -Caputo. For clarity, we present at the end an applied example to facilitate the clarification of the theoretical results obtained

A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives

“…Moreover, Wang et al [54] established the result of the average principle for FNSDEs in the pth moment. For further details regarding the averaging approach, see [55][56][57][58][59][60][61][62][63].…”