Work

Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator

Year: 2022

Type: article

Abstract: This paper formulates and solves a generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator. The fractional derivative is understood as the Gerasimov–Caputo derivative. The boundary conditions are given in the form of linear functionals, which makes it possible to cover a wide class of linear local and non-local conditions. A representation of the solution is found in terms of special functions. A necessary and sufficient condition for the solvability of the problem under study is obtained, as well as conditions under which the solvability condition is certainly satisfied. The theorem of existence and uniqueness of the solution is proved.

Source: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS

DOI: 10.31489/2022m2/108-116

Author: L.Kh. Gadzova

Institution: Federal State Budget Scientific Institution Institute of Applied Mathematics and Automation

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4283746041

FWCI: 1.02

Cites: 14

Cited by: 5

Related to: 10