论文标题
随机分数演算，并应用于变异原理
A Stochastic Fractional Calculus with Applications to Variational Principles
论文作者
论文摘要
我们引入了随机分数演算。作为一种应用，我们提出了变异的随机分数计算，该计算概括了变异对随机过程的分数计算。获得了随机分数Euler-Lagrange方程，扩展了文献中可用的经典，分数和随机计算的变化。为了说明我们的主要理论结果，我们讨论了两个示例：一个源自量子力学，第二个是通过足够的数值模拟验证的。
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.
