Work

Determining the order of time and spatial fractional derivatives

Year: 2024

Type: article

Abstract: The paper considers the initial‐boundary value problem for equation , in an N‐dimensional domain with a homogeneous Dirichlet condition. The fractional derivative is taken in the sense of Caputo. The main goal of the work is to solve the inverse problem of simultaneously determining two parameters: the order of the fractional derivative and the degree of the Laplace operator . A new formulation and solution method for this inverse problem are proposed. It is proved that in the new formulation the solution to the inverse problem exists and is unique for an arbitrary initial function from the class . Note that in previously known works, only the uniqueness of the solution to the inverse problem was proved and the initial function was required to be sufficiently smooth and non‐negative.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10393

Authors: Ravshan Ashurov, Ilyoskhuja Sulaymonov

Institutions: Academy of Sciences Republic of Uzbekistan, National University of Uzbekistan

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Ministry of Innovative Development of the Republic of Uzbekistan

Award: G2436033311