论文标题
希尔伯特空间中的进化方程
Evolution Equations in Hilbert Spaces via the Lacunae Method
论文作者
论文摘要
在本文中，我们考虑了在方程右侧施加的特殊条件下的抽象希尔伯特空间中的进化方程。我们建立了使我们能够制定存在和独特定理的方法，并在右侧的根矢量上以系列的形式找到解决方案。作为应用程序，我们考虑各种分数微分方程。 Riemann-Liouville分数差异操作员Riesz电位，差异操作员等运营商涉及到差异操作员。
In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and uniqueness theorem and find a solution in the form of a series on the root vectors of the right-hand side. As an application we consider fractional differential equations of various kinds. Such operators as the Riemann-Liouville fractional differential operator, the Riesz potential, the difference operator have been involved.
