2022/02/15 by Kukushkin, Maksim V.
#26A33 #39A05 #47A10 #47B10 #47B12 #47B28 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2202.07338
In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and uniqueness theorem and find a solution in the form of a series on the root vectors of the right-hand side. As an application we consider fractional differential equations of various kinds. Such operators as the Riemann-Liouville fractional differential operator, the Riesz potential, the difference operator have been involved.