Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 175–183. ISSN 2079-6641

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MSC 26A33, 35K57

Research Article

Numerical-analytical method for solving the modified Cauchy problem for the fractional diffusion equation

L. I. Serbina

GBOU VO Stavropol Stat Pedagogikal Institute, 355029, Stavropol, Lenina str, 417a, Russia


The paper considers a numerical-analytical method for efficient search for an approximate solution of the modified Cauchy problem for a parabolic differential equation with a fractional time derivative in the sense of Riemann-Liouville, which naturally arises in the study of nonlinear features of moisture-salt transfer processes in media with a fractal structure of pore space.

Key words: diffusion equation, fractal structure, fractional differentiation operator, numerical-analytical method, discrete analog, moisture transfer, algorithm.

DOI: 10.26117/2079-6641-2022-39-2-175–183

Original article submitted: 30.04.2022

Revision submitted: 02.06.2022

For citation. Serbina L. I. Numerical-analytical method for solving the modified Cauchy problem for the fractional diffusion equation. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 175–183. DOI: 10.26117/2079-6641-2022-39-2-175–183

Competing interests. The author declares that there are no conflicts of interest with respect to authorship and publication.

Contribution and responsibility. The author contributed to the writing of the article and is solely responsible for submitting the final version of the article to the press. The final version of the manuscript was approved by the author.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (

© Serbina L. I., 2022


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Serbina Lyudmila Ivanovna – D. Sci. (Phys. and Math.), Professor, Honorary Worker of the Higher Professional Education of the Russian Federation, Professor of the Department of Mathematics and Informatics of the State Pedagogical Institute in Stavropol, Russia, ORCID 0000-0003-3536-5846.