https://doi.org/10.26089/NumMet.v27r440

A difference scheme approximating a mixed boundary value problem for the heat equation with the Caputo–Fabrizio fractional time derivative

Authors

  • Kurbanmagomed R. Kadiev

Keywords:

fractional order derivative
heat equation
difference scheme
stability of difference scheme

Abstract

In recent years, fractional-differential calculus has been widely used to describe various physical processes in media with non-standard structures. In this regard, considerable attention is given to problems for partial differential equations of fractional order, which are a generalization of integer-order equations. Caputo and Fabrizio proposed a new fractional derivative without a singular kernel, which has useful properties for modeling in many scientific fields. In this paper, an initial-boundary value problem in a rectangular domain for the heat equation with the Caputo–Fabrizio fractional time derivative is investigated. An implicit difference scheme is constructed for the numerical solution of this problem. Using the method of energy inequalities, an a priori estimate for the solution is obtained. These inequalities ensure the stability of the scheme, the uniqueness of the solution and its continuous dependence on the input data. The convergence of the difference scheme to the solution of the original problem is proved. The conducted computational experiment confirmed the validity of the theoretical results.


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Published

2026-10-30

Issue

Vol. 27 (2026): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author

Kurbanmagomed R. Kadiev

Dagestan State University

• PhD Student

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