Geodesic
Parametric identification of Cauchy problem for one fractional differential equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 157-165

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The method for parametric identification of Cauchy problem for a fractional differential equation with fractional differential operator of $\alpha \in (0, 1)$ degree according to instantaneous values of experimental observations is suggested. The method is based on computation of mean-square estimations for coefficients of linear parametric discrete model of approximation function. Numerically-analytical investigations have been done, the results let us conclude about high efficiency of the method.
Keywords: fractional differential operators, parametric identification, linear parametric discrete model, difference equation. 
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     author = {A. S. Ovsienko},
     title = {Parametric identification of {Cauchy} problem for one fractional differential equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {157--165},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a15/}
}
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A. S. Ovsienko. Parametric identification of Cauchy problem for one fractional differential equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 157-165. http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a15/