Proceedings of the Internation Conference on "Humanities and Social Sciences: Novations, Problems, Prospects" (HSSNPP 2019)

Innovation Growth: Mathematical Modeling and Forecasting

Authors
D.V. Ivanov, E.A. Tikhomirov, E.B. Nazarenko, E.A. Andreeva, A.G. Ilmushkin, I.A. Grygoryants
Corresponding Author
D.V. Ivanov
Available Online July 2019.
DOI
https://doi.org/10.2991/hssnpp-19.2019.133How to use a DOI?
Keywords
innovation modeling, hereditary models, fractional calculus, errors in variables, least-squares fractional calculus, errors-in variables, least square method
Abstract
There is a lot of research into innovation modeling. This paper deals with long-memory models for innovation growth that are based on differential equations with fractional-order derivatives. Model parameters are, as a rule, unknown, and they are estimated with experimental data. The solutions to fractional-order differential equations discussed in this paper are nonlinear as far as some parameters are concerned. Estimating functions with non-linear parameters is a complicated problem. The authors propose algorithms for estimating the parameters of solutions to differential equations with fractional-order derivatives when there are errors in data. The paper presents two-step algorithms to estimate parameters for the innovation growth models under study. The first step involves matching the solution for a differential equation with nonlinear parameters to a linear difference equation. The second step involves estimating the linear coefficients of the solution to the differential equation. Test examples have shown that the proposed algorithms yield highly accurate estimates.
Open Access
This is an open access article distributed under the CC BY-NC license.

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Cite this article

TY  - CONF
AU  - D.V. Ivanov
AU  - E.A. Tikhomirov
AU  - E.B. Nazarenko
AU  - E.A. Andreeva
AU  - A.G. Ilmushkin
AU  - I.A. Grygoryants
PY  - 2019/07
DA  - 2019/07
TI  - Innovation Growth: Mathematical Modeling and Forecasting
BT  - Proceedings of the Internation Conference on "Humanities and Social Sciences: Novations, Problems, Prospects" (HSSNPP 2019)
PB  - Atlantis Press
SP  - 700
EP  - 704
SN  - 2352-5398
UR  - https://doi.org/10.2991/hssnpp-19.2019.133
DO  - https://doi.org/10.2991/hssnpp-19.2019.133
ID  - Ivanov2019/07
ER  -