The averaging principle of Hilfer fractional stochastic pantograph equations with non-Lipschitz conditions

Abstract

This paper is devoted to presenting an averaging principle for Hilfer fractional stochastic differential pantograph equations (HFSDPEs). The probability of the solutions to averaged stochastic systems in the means square sence can be used to approximate the solutions to HFSDPEs under appropriate non-Lipschitz conditions. Furthermore, certain previous results have been significantly generalised by our results. Finally, an example is given to demonstrate the feasibility of the results.