This article is cited in 4 papers

MATHEMATICS

Mixed boundary value problem for an ordinary differential equation with fractional derivatives with different origins

L.M. Eneeva<sup>ab

a</sup> Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center
^b Kabardino-Balkar State University, Nal'chik

Abstract: A mixed boundary value problem is solved for an ordinary differential equation containing a composition of left- and right-sided Riemann-Liouville and Caputo fractional differentiation operators. The problem is equivalently reduced to a Fredholm integral equation of the second kind, for which a sufficient condition for unique solvability is found. As a consequence, the Lyapunov inequality is proved for the problem under study.

Keywords: fractional differential equation with different origins, mixed boundary value problem, Riemann-Liouville derivative, Caputo derivative.

UDC: 517.95

MSC: 26A33

DOI: 10.26117/2079-6641-2021-36-3-65-71

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