SOLVABILITY OF THE CAUCHY PROBLEM FOR EQUATIONS WITH RIEMANN–LIOUVILLE’S FRACTIONAL DERIVATIVES
https://doi.org/10.29235/1561-8323-2018-62-4-391-397
Abstract
In this article we study the solvability of the analogue of the Cauchy problem for ordinary differential equations with Riemann–Liouville’s fractional derivatives with a nonlinear restriction on the right-hand side of functions in certain spaces. The conditions for solvability of the problem under consideration in given function spaces, as well as the conditions for existence of a unique solution are given. 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.
About the Authors
Petr P. Zabreiko
Belarusian State University
Belarus
Belarus
Zabreiko Petr Petrovich – D. Sc. (Physics and Mathematics), Professor
4, Nezavisimosti Ave., 220030, Minsk
Svetlana V. Ponomareva
Belarusian State University
Belarus
Belarus
Ponomareva Svetlana Vladimirovna – Ph. D. (Physics and Mathematics), Assistant Professor
4, Nezavisimosti Ave., 220030, Minsk
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