We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on \({\mathbb {R}}\), we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.

中文翻译：

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分数阶微分方程的希尔伯特空间方法

我们研究希尔伯特空间中Riemann–Liouville和Caputo型的分数阶微分方程。使用在\（{\ mathbb {R}} \）上定义的函数的指数加权空间，我们通过使用傅立叶变换的函数演算来定义分数运算符。主要工具是外推和内插空间。主要结果是非线性分数阶微分方程解的存在和唯一性以及解算子的因果关系。