一类分数阶积分-微分Langevin方程初值问题解的存在唯一性

Existence and uniqueness of solutions of initial value problems for fractional integro-differential Langevin equation

该文研究含3个分数阶导数的非线性积分-微分Langevin方程初值问题.首先应用Schauder不动点定理得到了解的存在性结果,然后运用Banach压缩映射原理建立了解的唯一性,最后举例说明了主要结果的应用.

In this paper,the solvability of initial value problems for fractional integro-differential Langevin equation involving three fractional orders is discussed.First,by means of Schauder fixed point theorem,an existence result for the solution is obtained.Then,the unique solution is established using the Banach contraction mapping principle.Finally,an example is provided to illustrate the main results.