
Some methods for solving equations with an operator function and applications for problems with a fractional power of an operator
Several applied problems are characterized by the need to numerically so...
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Approximate representation of the solutions of fractional elliptical BVP through the solution of parabolic IVP
Boundary value problem for a fractional power of an elliptic operator is...
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Solving timefractional differential equation via rational approximation
Fractional differential equations (FDEs) describe subdiffusion behavior ...
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Regularization of a backwards parabolic equation by fractional operators
The backwards diffusion equation is one of the classical illposed inver...
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Controllability properties from the exterior under positivity constraints for a 1D fractional heat equation
We study the controllability to trajectories, under positivity constrain...
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Research of the hereditary dynamic Riccati system with modification fractional differential operator of GerasimovCaputo
In this paper, we study the Cauchy problem for the Riccati differential ...
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Approximation of the spectral fractional powers of the LaplaceBeltrami Operator
We consider numerical approximation of spectral fractional LaplaceBeltr...
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Splitting Schemes for NonStationary Problems with a Rational Approximation for Fractional Powers of the Operator
Problems of the numerical solution of the Cauchy problem for a firstorder differentialoperator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the selfadjoint positive operator. In computational practice, rational approximations of the fractional power operator are widely used in various versions. The purpose of this work is to construct special approximations in time when the transition to a new level in time provided a set of standard problems for the operator and not for the fractional power operator. Stable splitting schemes with weights parameters are proposed for the additive representation of rational approximation for a fractional power operator. Possibilities of using similar time approximations for other problems are noted. The numerical solution of a twodimensional nonstationary problem with a fractional power of the Laplace operator is also presented.
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