Boykov Il'ya Vladimirovich, Doctor of physical and mathematical sciences, professor, head of sub-department of higher and applied mathematics, Penza State University (Penza, 40 Krasnaya str.), firstname.lastname@example.org
Krivulin Nikolay Petrovich, Candidatе of physical and mathematical sciences, associate professor, sub-department of higher and applied mathematics, Penza State University (Penza, 40 Krasnaya str.), email@example.com
The authors suggest a method of parameters identification for dynamic systems, the functioning of which is simulated by the differential equations with fraction order partial derivatives with temporary and spatial variables
A∂oαtu(t, x) = B∂βoxu(t, x) + g(t, x), with entry k (0, ) ( ), ot u x ak x ∂α− = k =1,2,..., m = [α]+1, and boundary conditions k ( ,0) ( ), ot u t bk t ∂β− = k =1,2,...,n = [β]+1. To determine A, B, α, β parameters to the initial problem the authors use the Laplace integral transformation and the sought parameters are determined by the least square method in the spectral domain. The suggested method may be applied to differential equations in partial derivatives of integral order, in particular, to elliptical, hyperbolic and parabolic equations. The article adduces model examples demonstrating high efficiency of the method. The researchers suggest a method of parameter identification for dynamic systems, described by differential equations with partial derivatives of fraction orders. The suggested method may be applied in various universes of discourse: information measuring technology, thermal conductivity, chemistry, astrophysics etc.
differential equations with partial derivatives of fraction order, hereditiary systems, distributed systems, parametric identification, parameter identification.
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