The existence and averaging principle for stochastic fractional differential equations with impulses
Jing Zou, Danfeng Luo, Mengmeng Li
Abstract
In this paper, a class of fractional stochastic differential equations (SFDEs) with impulses is considered. By virtue of Mönch's fixed point theorem and Banach contraction principle, we explore the existence and uniqueness of solutions to the addressed system. Furthermore, with the aid of the Jensen inequality, Hölder inequality, Burkholder–Davis–Gundy inequality, Grönwall–Bellman inequality, and some novel assumptions, the averaging principle of our considered system is obtained. At the end of this paper, an example is provided to illustrate the theoretical results.
Topics & Concepts
MathematicsContraction principleUniquenessFixed-point theoremBanach fixed-point theoremInequalityMathematical analysisContraction (grammar)Stochastic differential equationApplied mathematicsMathematical economicsInternal medicineMedicineFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems