(Differencialnie Uravnenia i Protsesy Upravlenia)

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Русская версия

**M. KH. Beshtokov**

Department of Computational Methods,

Institute of Applied Mathematics and Automation,

Kabardino-Balkarskii Scientific center RAS

We study boundary value problems for a spatially one-dimensional loaded moisture transfer equation of fractional-order with nonlocal boundary conditions. Using the method of energy inequalities, and assuming the existence of a solution of the problem, we derive a priori estimates for the solutions of nonlocal boundary value problems in differential form. Difference schemes are constructed and analogues of a priori estimates in difference form are proved for them; error estimates are given under the assumption of sufficient smoothness of the solutions of the equation. From the obtained a priori estimates, the uniqueness and stability of the solution with respect to the initial data and the right-hand side follow, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at the rate equal to the approximation order of the difference problem.

- a priori estimate
- Caputo fractional derivative
- fractional differential equation
- Hallaire's equation
- loaded equation
- moisture transfer equation
- nonlocal boundary value problems

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- Beshtokov, M. KH. On the numerical solution of a nonlocal boundary value problem for a degenerating pseudoparabolic equation // Differential Equations, 52:10 (2016), 1341-1354
- Beshtokov, M. KH. Difference method for solving a nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients // Comput. Math. Math. Phys., 56:10 (2016), 1763-1777
- Beshtokov, M. KH. Differential and difference boundary value problem for loaded third-order pseudo-parabolic differential equations and difference methods for their numerical solution // Comput. Math. Math. Phys., 57:12 (2017), 1973-1993
- Beshtokov, M. KH. Local and nonlocal boundary value problems for degenerating and nondegenerating pseudoparabolic equations with a Riemann-Liouville fractional derivative // Differential Equations, 54:6 (2018), 758-774
- Beshtokov, M. KH. Boundary value problems for a pseudoparabolic equation with the Caputo fractional derivative // Differential Equations, 55:7 (2019), 1-10
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- Alikhanov, A. A. A new difference scheme for the time fractional diffusion equation. // Journal of computational physics, 280 (2015), 424-438
- Beshtokov, M. KH. To boundary-value problems for degenerating pseudoparabolic equations with Gerasimov-Caputo fractional derivative // Russian Mathematics, 62:10 (2018), 1-14
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