Email this article ABOUT AN ESTIMATE FROM ABOVE OF THE FRACTIONAL DERIVATIVE OF THE COMPOSITION OF TWO FUNCTIONS
- Authors: Gomoyunov M.I.1
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Affiliations:
- N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
- Issue: Vol 23, No 122 (2018)
- Pages: 261-267
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/297230
- DOI: https://doi.org/10.20310/1810-0198-2018-23-122-261-267
- ID: 297230
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Abstract
In the paper, an estimate from above of the fractional Riemann-Liouville derivative of an order α∈0;1 of the composition of two functions is proved for the case when the inner function is assumed only to be represented by the fractional Riemann-Liouville integral of a measurable essentially bounded function. The necessity of such an estimate arises in control problems of dynamical systems described by differential equations with fractional derivatives.
Full Text
Пусть [a, b] ⊂ R, n ∈ N и заданы функции V : Rn → R и x : [a, b] → Rn. Рассмотрим их композицию v(t) = V (x(t)), t ∈ [a, b].×
About the authors
Mikhail Igorevich Gomoyunov
N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
Email: m.i.gomoyunov@gmail.com
Candidate of Physics and Mathematics, Senior Researcher of the Dynamical Systems Department 16 S. Kovalevskaya St., Yekaterinburg 620990, Russian Federation
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