Nakhushev extremum principle for integro-differential operators

In this paper, we prove the extremum principle for an integro-differential operator with a kernel of a general form, which generalizes an analog of Fermat's extremum theorem for the Riemann–Liouville fractional derivative. Also, we formulate the weighted extremum principle and the extremum principles for integro-differential operators of convolution type and for some fractional differentiation operators.