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.
Editorial Note: This paper has been presented at the online international conference “WFC 2020: Workshop on Fractional Calculus”, Ghent University, Belgium, 9–10 June 2020.
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