This article is cited in 7 papers

MATHEMATICS

Lyapunov inequality for an equation with fractional derivatives with different origins

L M. Eneeva

Institute of Applied Mathematics and Automation, 360000, Nalchik, Shortanova st., 89 A, Russia

Abstract: We consider an ordinary differential equation of fractional order with the composition of left and rightsided fractional derivatives, which is a model equation of motion in fractal media. We find a necessary condition for existence of nontrivial solution of homogeneous Dirichlet problem for the equation under consideration. The condition has the form of integral estimate for the potential and is an analog of Lyapunov inequality.

Keywords: Riemann-Liouville fractional derivative, Caputo fractional derivative, Dirichlet problem, Lyapunov inequality.

UDC: 517.927

MSC: 26A33

DOI: 10.26117/2079-6641-2019-28-3-32-39