Cauchy problem for the equations with fractional of Riemann-Liouville derivatives
https://doi.org/10.29235/1561-8323-2020-64-1-13-20
Abstract
In this article, we study the question of the solvability of an analogue of the Cauchy problem for ordinary differential equations with fractional Riemann-Liouville derivatives on the unbounded right-hand side in certain function spaces. The solvability conditions of the problem under consideration in given function spaces, as well as the existence conditions of a unique solution are presented. The study uses the method of reducing the problem to the second-kind Volterra equation, the Schauder principle of a fixed point in a Banach space, and the Banach-Cachoppoli principle of a fixed point in a complete metric space.
Supporting agencies: The authors are very grateful to Professor A. B. Antonevich, Chair of Functional Analysis and Economics, for multiple discussions of the obtained results and a number of valuables advices
About the Authors
P. P. Zabreiko
Belarusian State University
Belarus
Belarus
Petr P. Zabreiko
S. V. Ponomareva
Belarusian State University
Belarus
Belarus
Ponomareva Svetlana V. - Ph. D. (Physics and Mathematics), Associate professor.
4, NezavisimostiAve., 220050, MinskReferences
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