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.), email@example.com
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.), firstname.lastname@example.org
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.
1. Nakhushev A. M. Drobnoe ischislenie i ego primenenie [Fractional calculation and application thereof]. Moscow: Fizmatlit, 2003, 272 p.
2. Samko S. G., Kilbas A. A., Marychev O. I. Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya [Integrals and derivatives of fraction order and several applications thereof]. Minsk: Nauka i tekhnika, 1987, 688 p.
3. Uchaykin V. V. Metod drobnykh proizvodnykh [Fractional derivatives method]. Ulyanovsk: Artishok, 2008, 512 p.
4. Boykov I. V., Krivulin N. P. Izmeritel'naya tekhnika [Measuring technology]. 2000, no. 9, pp. 29–32.
5. Boykov I. V., Krivulin N. P. Metrologiya [Metrology]. 2012, no. 8, pp. 3–14.
6. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya: uchebnik. pod red. K. A. Pupkova, N. D. Egupova [Methods of classical and modern theory of automatic control: textbook edited by K. A. Pupkov, N. D. Egupov]. Moscow: Izdatel'stvo MGTU im. N. E. Baumana, 2004, vol. 1, 656 p. ; vol. 2, 640 p. ; vol. 3, 616 p. ; vol. 4, 744 p. ; vol. 5, 784 p.