Abstract We investigate extreme properties of a class of integro-differential operators. We prove an assertion that extends the Nakhushev extremum principle, known for fractional Riemann-Liouville derivatives, to integro-differential operators with kernels of a general form. We establish the weighted extremum principle for convolution operators and the Riemann-Liouville fractional derivative. In addition, as an application, we prove a uniqueness theorem for a boundary value problem in a non-cylindrical domain for the fractional diffusion equation with the Riemann-Lioville fractional derivative.

中文翻译：

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一类积分微分算子的 Nakhushev 极值原理

摘要 我们研究了一类积分微分算子的极端性质。我们证明了一个断言，该断言将 Nakhushev 极值原理（以分数 Riemann-Liouville 导数而闻名）扩展到具有一般形式核的积分微分算子。我们建立了卷积算子的加权极值原理和 Riemann-Liouville 分数阶导数。此外，作为应用，我们证明了具有 Riemann-Lioville 分数阶导数的分数阶扩散方程的非圆柱域中边值问题的唯一性定理。