Open AccessSOLVABILITY OF THE CAUCHY PROBLEM FOR EQUATIONS WITH RIEMANN–LIOUVILLE’S FRACTIONAL DERIVATIVES
Author(s) -
П. П. Забрейко,
С. В. Пономарева
Publication year - 2018
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2018-62-4-391-397
Subject(s) - mathematics , banach space , cauchy–riemann equations , fixed point theorem , initial value problem , mathematical analysis , cauchy problem , complete metric space , pure mathematics , fractional calculus , ordinary differential equation , space (punctuation) , nonlinear system , differential equation , linguistics , philosophy , physics , quantum mechanics
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.