Оператор
A non-local problem for a mixed type equation with partial fractional derivative of Riemann – Liouville is studied, boundary condition of which contains linear combination of generalized operators of fractional integro-differentiation. Unique solvability of the problem is then proved.
With the use of operators from approximation function theory we construct integral operators with discontinuous range of values, which make it possible to obtain uniform approximations of continuous functions on the whole interval of their definition.
The paper deals with necessary and sufficient conditions of uniform convergence of generalized Riesz means for the expansions in eigen and associated functions of the 1-st order functional-differential operator on the graph with three ribs forming a cycle.
An integral operator representable as the sum of a Volterra operator and one-dimensional one is considered, when the inverse operator for Volterra one is an integro-differential operator of second order. The inverse problem of reconstruction of the one-dimensional item from spectral data provided that the Volterra component is known a priori is investigated. The uniqueness of the solution of the inverse problem is proved and conditions are obtained that are necessary and sufficient for its solvability.
