| Issue |
E3S Web Conf.
Volume 474, 2024
X International Annual Conference “Industrial Technologies and Engineering” (ICITE 2023)
|
|
|---|---|---|
| Article Number | 02027 | |
| Number of page(s) | 15 | |
| Section | Applied IT Technologies in Energy and Industry | |
| DOI | https://doi.org/10.1051/e3sconf/202447402027 | |
| Published online | 08 January 2024 | |
To boundary value problems for a generalized hyperbolic equation with two fractional differentiation operators
Institute of Applied Mathematics and Automation, KBSC RAS, 360000 Nalchik, Russia
* Corresponding author: beshtokov-murat@yandex.ru
Boundary value problems for a one-space-dimensional hyperbolic equation with two fractional differentiation operators and variable coefficients are considered. The method of finite differences is used for the approximate solution to the problems posed. Difference schemes for each of the problems are constructed, and by the method of energy inequalities for various relations between the orders of the fractional derivative (α, β) a priori estimates in differential and difference interpretations are obtained. The obtained estimates imply the uniqueness and stability of the solution with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem. Algorithms for the numerical solution of the problems posed are constructed.
© The Authors, published by EDP Sciences, 2024
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