Development of identification methods for fractional differential equations with riemann-liouville fractional derivative
The methods for parametric identification of fractional differential operators with $\alpha \on (1, 2)$ degree according to instantaneous values of experimental observations based on the Barrett differential equation example are suggested. The methods are based on construction of the linear parametri...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2014-03-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20735/16995 |
| _version_ | 1828414359774167040 |
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| author | Anna S Ovsienko |
| author_facet | Anna S Ovsienko |
| author_sort | Anna S Ovsienko |
| collection | DOAJ |
| description | The methods for parametric identification of fractional differential operators with $\alpha \on (1, 2)$ degree according to instantaneous values of experimental observations based on the Barrett differential equation example are suggested. The methods are based on construction of the linear parametrical discrete model for fractional differential equation. The coefficients of the model are associated with the required parameters of differentiation equation of fractional order. Different approaches to the determination of the relationships between the parameters of the differential equation and the discrete model coefficients are considered. Connection expressions for coefficients of linear parametrical discrete model and Cauchy type problem parameters to be identified are obtained. The algorithm of the method which let us reduce the problem to computation of mean-square estimates for coefficients of linear parametrical discrete model is described. Numerical investigations have been done; furthermore, their results let us conclude high efficiency of the methods. |
| first_indexed | 2024-12-10T13:24:50Z |
| format | Article |
| id | doaj.art-cf410bd82343410d95fbc3f4858a3b70 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:24:50Z |
| publishDate | 2014-03-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-cf410bd82343410d95fbc3f4858a3b702022-12-22T01:47:13ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812014-03-0118113414410.14498/vsgtu127218153Development of identification methods for fractional differential equations with riemann-liouville fractional derivativeAnna S Ovsienko0Samara State Technical UniversityThe methods for parametric identification of fractional differential operators with $\alpha \on (1, 2)$ degree according to instantaneous values of experimental observations based on the Barrett differential equation example are suggested. The methods are based on construction of the linear parametrical discrete model for fractional differential equation. The coefficients of the model are associated with the required parameters of differentiation equation of fractional order. Different approaches to the determination of the relationships between the parameters of the differential equation and the discrete model coefficients are considered. Connection expressions for coefficients of linear parametrical discrete model and Cauchy type problem parameters to be identified are obtained. The algorithm of the method which let us reduce the problem to computation of mean-square estimates for coefficients of linear parametrical discrete model is described. Numerical investigations have been done; furthermore, their results let us conclude high efficiency of the methods.https://journals.eco-vector.com/1991-8615/article/viewFile/20735/16995fractional differential operatorsparametric identificationlinear parametrical discrete modeldifference equation |
| spellingShingle | Anna S Ovsienko Development of identification methods for fractional differential equations with riemann-liouville fractional derivative Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki fractional differential operators parametric identification linear parametrical discrete model difference equation |
| title | Development of identification methods for fractional differential equations with riemann-liouville fractional derivative |
| title_full | Development of identification methods for fractional differential equations with riemann-liouville fractional derivative |
| title_fullStr | Development of identification methods for fractional differential equations with riemann-liouville fractional derivative |
| title_full_unstemmed | Development of identification methods for fractional differential equations with riemann-liouville fractional derivative |
| title_short | Development of identification methods for fractional differential equations with riemann-liouville fractional derivative |
| title_sort | development of identification methods for fractional differential equations with riemann liouville fractional derivative |
| topic | fractional differential operators parametric identification linear parametrical discrete model difference equation |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20735/16995 |
| work_keys_str_mv | AT annasovsienko developmentofidentificationmethodsforfractionaldifferentialequationswithriemannliouvillefractionalderivative |