Innovation Growth: Mathematical Modeling and Forecasting
D.V. Ivanov, E.A. Tikhomirov, E.B. Nazarenko, E.A. Andreeva, A.G. Ilmushkin, I.A. Grygoryants
Available Online July 2019.
- https://doi.org/10.2991/hssnpp-19.2019.133How to use a DOI?
- innovation modeling, hereditary models, fractional calculus, errors in variables, least-squares fractional calculus, errors-in variables, least square method
- 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.
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 -