Work

Non-Local Problems for the Fractional Order Diffusion Equation and the Degenerate Hyperbolic Equation

Year: 2024

Type: article

Abstract: In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8090538

Authors: Menglibay Ruziev, Roman Parovik, Rakhimjon Zunnunov, Nargiza Yuldasheva

Institutions: Academy of Sciences Republic of Uzbekistan, Institute of Cosmophysical Research and Radio Wave Propagation, Gubkin Russian State University of Oil and Gas

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funders: Academy of Sciences Republic of Uzbekistan, Russian Academy of Sciences