Correct solvability of problems for fractional-power operator equations

S. D. Baboshin

Voronezh State University, Voronezh, Russia

Abstract: In this paper, we consider the sum of linear fractional-power operators acting in a Banach space and satisfying weak positivity. We establish the correct solvability of the problem for the corresponding fractional-operator equation and we give the representation of the solution through the inverse operator with an exact estimate of its norm. The results are applied to problems without initial conditions for an equation with singular coefficients. We consider examples of such equations.

Keywords: fractional power operator, fractional-operator equation, correct solvability.

UDC: 517.98

DOI: 10.22363/2413-3639-2024-70-4-533-541