A new result on averaging principle for Caputo-type fractional delay stochastic differential equations with Brownian motion
Jing Zou, Danfeng Luo
Abstract
In this paper, we mainly explore the averaging principle of Caputo-type fractional delay stochastic differential equations with Brownian motion. Firstly, the solutions of this considered system are derived with the aid of the Picard iteration technique along with the Laplace transformation and its inverse. Secondly, we obtain the unique result by using the contradiction method. In addition, the averaging principle is discussed by means of the Burkholder-Davis-Gundy inequality, Jensen inequality, Hölder inequality and Grönwall-Bellman inequality under some hypotheses. Finally, an example with numerical simulations is carried out to prove the relevant theories.
Topics & Concepts
MathematicsStochastic differential equationType (biology)Fractional Brownian motionConstructiveApplied mathematicsGeometric Brownian motionLaplace transformInequalityBrownian motionCalculus (dental)Mathematical economicsMathematical analysisDiffusion processComputer scienceStatisticsBiologyMedicineEcologyOperating systemProcess (computing)Innovation diffusionKnowledge managementDentistryFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods